Journal of Marine Science and Engineering

Article Relationship between the Persian Gulf -Level Fluctuations and Meteorological Forcing

Naghmeh Afshar-Kaveh 1,* , Mostafa Nazarali 2 and Charitha Pattiaratchi 3

1 School of Civil Engineering, Iran University of science and technology, Tehran 16846-13114, Iran 2 Department of Coastal Engineering, Pouya Tarh Pars Consulting Engineers Company, Tehran 14376-15613, Iran; [email protected] 3 Graduate School & the UWA Oceans Institute, The University of Western Australia, Perth 6009, Australia; [email protected] * Correspondence: [email protected]; Tel.: +98-91-2325-5481

 Received: 14 February 2020; Accepted: 13 April 2020; Published: 16 April 2020 

Abstract: Sea-level data from six gauge stations along the northern coast of the Persian Gulf were analyzed both in time and frequency domain to evaluate meteorological forcing. Spectral analyses indicated that mixed, predominantly semi-diurnal were dominant at all stations, but low-frequency fluctuations correlated well with atmospheric pressure and wind components. Non-tidal sea-level fluctuations up to 0.75 m were observed along the northern coasts of the Gulf due to the combined action of lower atmospheric pressure and cross-shore wind. Coherency between low-frequency sea-level records and mean sea-level pressure indicated that the latter usually leads to sea-level fluctuations between 1 and 6.4 days. In contrast, the same analysis on the wind velocity and revealed that the former lags between 3 and 13 days. The effect of wind stress on coastal sea-level variations was higher compared with the effect of atmospheric pressure. Concurrent analysis of low-pass-filtered sea-level records proved that the non-tidal wave moves from west to east along the northern coasts of the Persian Gulf.

Keywords: sea level; wind velocity; atmospheric pressure; spectral analysis

1. Introduction Coastal regions experience sea-level fluctuations occurring over different time scales from seconds to centuries. Globally, astronomical forces of the Sun and the Moon result in tidal variability with periods of 12 and 24 h as well as tidal modulations with periods up to 18.6 years [1,2]. In many regions, the effects of the tides dominate the water-level variability. However, in regions where the tidal effects are smaller, other processes, such as atmospheric forcing, are important for determining the local water level. The relative importance of air pressure and winds in sea-level variability depends on the location and time scale [3]. The sea surface will rise in response to a drop in local air pressure, and vice versa, which is called the local inverse barometer (LIB). In the ideal LIB model a rise/fall of 1 mbar in air pressure results in a fall/rise of 1 cm in sea level [1]. However, this isostatic condition rarely applies to coastal [4]. In addition, atmospheric pressure is not the only meteorological forcing responsible for sea-level variability. Winds blowing over the shallow waters result in wind set-up/set-down. Sea-level variability (SLV) in response to wind and atmospheric pressure change has been extensively studied for different water bodies around the world [5–7]. They are considered to be meso-scale phenomena both temporally and spatially [8]. In these studies, observed records of sea-level fluctuations were compared with atmospheric pressure and wind observations both in time and frequency domains. In contrast, some authors employed soft computing methods [9,10] or

J. Mar. Sci. Eng. 2020, 8, 285; doi:10.3390/jmse8040285 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 285 2 of 16 circulation models [11–13] to investigate the relationship between meteorological forces and the sea-level fluctuations. However, these types of sea-level fluctuations due to atmospheric forcing have received less attention in the Persian Gulf. Although occurrences of tropical cyclones have never been recorded in the Persian Gulf, there may be such events in the future associated with global warming [14]. One of the most recent destructive events in the region was recorded on 19 March 2017. This was a meteorological [15] that hit the shorelines of Dayyer coastal city along the northern coast of the Gulf [16]. During this event, the maximum run-up of 3 m and inundation of about one kilometer resulted in five people dying. Atmospheric processes that generate SLV encompass a variety of temporal and spatial scales, and their contribution to sea-level extremes may vary spatially and temporally. The response of sea level to meteorological forces can be described by means of depth-integrated equations of motions. The change in sea level, ∆η, in response to an atmospheric pressure change ∆Pa and wind can be written as: ∆Pa ∆η = − (1) ρg

∆η τy = (2) ∆y ρg(η + h) where Pa is atmospheric pressure, τy is wind stress, ρ and g are density and gravitational acceleration, respectively. h is the water depth. In this paper, we examine the SLV along the northern coasts of the Persian Gulf, with the aim of identifying the contribution of atmospheric pressure and wind to low-frequency sea-level fluctuations. Sea-level data from 6 tide gauges along the northern Persian Gulf coasts were used to evaluate different types of sea-level fluctuations in the region. In addition, frequency analysis on the meteorological forces, including atmospheric pressure, and wind velocity components are presented in this paper. The coherency between these forces is also described both in time and frequency domains.

2. Materials and Methods

2.1. Study Area The study area is the Persian Gulf, a semi-enclosed basin with the maximum depth of 90 m and area of 251,000 km2. This Gulf is connected to the Gulf of Oman in the east by the Strait of Hormuz. The sea-level data were available at 6 stations along the northern coast of the Persian Gulf (Figure1). Some of these stations are operated by the National Cartographic Center of Iran and the others were installed during temporary projects by Port and Maritime Organization of Iran. The sampling interval of sea-level observations at Kangan and Bushehr was 30 min and 10 min in others (Table1). The mean varied from 1.5 m in Bushehr to 0.9 m in Javad al-Aemmeh. The maximum tidal range (difference between the highest and the lowest astronomical tide) at these stations were 3.26 m and 1.65 m, respectively. J. Mar. Sci. Eng. 2020, 8, 285 3 of 16

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Figure 1.1. Location of sea-levelsea‐level observations (red triangles) and meteorology stations (yellow boxes) locatedlocated alongalong the the northern northern coasts ofcoasts the Persian of the Gulf Persian (Image fromGulf Google (Image Map: from https: Google//goo.gl /mapsMap:/ MAU6TJCNbFGXoDzU6https://goo.gl/maps/MAU6TJCNbFGXoDzU6).).

Table 1.1. Sea-levelSea‐level data along northern Persian GulfGulf coasts.coasts.

StationStation NameName Start Start Finish Finish Time Time Step Step (min) Duration Duration (days) (days) DeylamDeylam 11 11 July July 2010 2010 11 11 February February 2011 2011 10 10 215 215 BushehrBushehr 3030 September September 2008 2008 30 30 September September 2010 2010 3030 729 729 LavarLavar 24 24 June June 2010 2010 3 3 October October 2010 2010 10 10 101 101 KanganKangan 3030 September September 2008 2008 30 30 September September 2010 2010 3030 729 729 JavadJavad al-Aemmehal‐Aemmeh 14 14 April April 2010 2010 5 5 July July 2010 2010 10 10 81 81 BostanehBostaneh 2525 November November 2009 2009 1818 August August 2010 2010 10 10 265 265

2.2. Data Sources Data on atmosphericatmospheric parameters including winds (speed and direction) and MeanMean Sea-LevelSea‐Level Pressure (MSLP)(MSLP) were were obtained obtained from from two two sources: sources: (1) coastal(1) coastal meteorology meteorology stations stations [17]; and, [17]; (2) and, global (2) weatherglobal weather prediction prediction model, model, European European Center Center for Medium-Range for Medium‐Range Weather Weather Forecasts Forecasts (ECMWF) (ECMWF) [18]. In[18]. this In study,this study, the latterthe latter set wereset were chosen chosen for for further further analysis. analysis. This This was was because because location location ofof coastalcoastal meteorology stations (Figure 11)) were were far far away away from from the the tide gauge stations. stations. Also, Also, the the sampling sampling intervalinterval at these these stations stations was was three three hours hours with with many many gaps gaps in the in the records records and and were were located located inland. inland. The TheECMWF ECMWF ERA5 ERA5 data set data were set available were available at hourly at hourly intervals intervals over a 0.25° over grid. a 0.25 Although◦ grid. Although these data these may dataunderestimate may underestimate some peak some values peak due values to the due temporal to the temporal and spatial and averaging. spatial averaging. Comparison Comparison between betweenERA5 and ERA5 meteorology and meteorology station wind station speeds wind indicated speeds that indicated for both that wind for components both wind components at all stations, at allthe stations, mean correlation the mean coefficient correlation was coe 0.68.fficient The was Root 0.68. Mean The Square Root Mean Error Square(RMSE) Error in these (RMSE) stations in thesewere −1 1 stationsbetween were 2 and between 2.75 ms 2 and. The 2.75 same ms− comparisons. The same comparisonswere performed were for performed MSLP data for MSLPof ERA5 data and of ERA5meteorology and meteorology stations and stations the mean and correlation the mean correlationcoefficient and coe ffiRMSEcient at and the RMSE stations at thewere stations 0.99 and were 0.6 0.99hPa, and respectively. 0.6 hPa, respectively. The dominant wind in the Persian Gulf is the Shamal wind, a north‐westerly wind that blows most of the time and change its direction while moving to the east [19]. A snapshot of a Shamal wind event affecting the whole Persian Gulf on 22 January 2010 is shown in Figure 2. The background of

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The dominant wind in the Persian Gulf is the Shamal wind, a north-westerly wind that blows most of the time and change its direction while moving to the east [19]. A snapshot of a Shamal wind J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 16 event affecting the whole Persian Gulf on 22 January 2010 is shown in Figure2. The background of this image shows the terrainterrain map of thethe landland surroundingsurrounding thethe PersianPersian Gulf.Gulf. It is clear that thethe wind aligns itself parallel parallel to to the the longitudinal longitudinal axis axis of of the the Gulf. Gulf. As As is shown is shown on onthis this image, image, moving moving from from the thewest west toward toward east, east, the wind the wind vectors vectors propagate propagate parallel parallel to the to mountains the mountains that are that mainly are mainly located located along alongthe northern the northern part of part the ofGulf. the The Gulf. second The second important important wind in wind this inregion this regionis called is Kaus called (Sharqi) Kaus (Sharqi) wind, wind,which which blows blowsfrom southeast. from southeast. The frequency The frequency of occurrence of occurrence of Kaus of winds Kaus is winds lower is than lower Shamal than Shamal winds, winds,but their but maximum their maximum wind speed wind is speed higher. is Overall, higher. Overall, the percentage the percentage of calm wind of calm (wind wind speed (wind < 2 speed ms−1) 1

Figure 2. WindWind velocity velocity vectors vectors over over the the Persian Persian Gulf Gulf showing showing a typical a typical Shamal Shamal wind wind event event (22 (22January January 2010). 2010). The MSLP in the study region varied between 989.7 hPa (summer) and 1028.0 hPa (winter) with a The MSLP in the study region varied between 989.7 hPa (summer) and 1028.0 hPa (winter) with mean of 1008.6 hPa. The highest decrease of MSLP during a week was 15 hPa that coincided with the a mean of 1008.6 hPa. The highest decrease of MSLP during a week was 15 hPa that coincided with passage of weather fronts over the Persian Gulf (Figure3). the passage of weather fronts over the Persian Gulf (Figure 3).

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Figure 3. ((aa)) Time Time series series of of mean mean sea sea-level‐level pressure pressure at at Bushehr Bushehr station station during 2009–2010; 2009–2010; ( (b)) an event event inin February 2010 with decreasing MSLP; and, (c) an event increasing MSLP inin JulyJuly 2010. 3. Results 3. Results In this paper, we are going to focus on the contribution of atmospheric forcing on the sea-level In this paper, we are going to focus on the contribution of atmospheric forcing on the sea‐level variations within Persian Gulf. Therefore, at the first step, the behavior of atmospheric forcing and variations within Persian Gulf. Therefore, at the first step, the behavior of atmospheric forcing and sea-level records were studied separately. Then the combined relationship between these parameters sea‐level records were studied separately. Then the combined relationship between these parameters was examined. was examined. 3.1. Spectral Analysis 3.1. Spectral Analysis Before investigation on the periodicity of wind, the hourly winds vector data were decomposed Before investigation on the periodicity of wind, the hourly winds vector data were decomposed into the major and minor components [20]. The principal axis of wind velocity in all stations was into the major and minor components [20]. The principal axis of wind velocity in all stations was parallel to the shoreline, along the longitudinal axis of the Persian Gulf. Therefore, the major component parallel to the shoreline, along the longitudinal axis of the Persian Gulf. Therefore, the major is the along-shore wind velocity component while the minor one is the cross-shore wind velocity component is the along‐shore wind velocity component while the minor one is the cross‐shore wind component. It must be emphasized that both along-shore and cross-shore wind velocity components velocity component. It must be emphasized that both along‐shore and cross‐shore wind velocity could affect sea-level height at the coastal regions. The contribution of cross-shore component was components could affect sea‐level height at the coastal regions. The contribution of cross‐shore described by Equation (2). The energy spectrum of the wind velocity components was calculated for component was described by equation 2. The energy spectrum of the wind velocity components was each station (Figure4). The analysis of wind velocity variations for time scales ranging from 2 h to one calculated for each station (Figure 4). The analysis of wind velocity variations for time scales ranging year, indicated periodicity in some frequencies. The highest peaks in the spectrum corresponded to from 2 h to one year, indicated periodicity in some frequencies. The highest peaks in the spectrum 24 h, representing sea breezes activity [21]. A complementary spectral peak occurs at the first harmonic corresponded to 24 h, representing sea breezes activity [21]. A complementary spectral peak occurs of the diurnal frequency, period of 12 h, which is due to the occurrence of land breezes. A large amount at the first harmonic of the diurnal frequency, period of 12 h, which is due to the occurrence of land of energy is present at the low-frequency part of the spectrum whose periods are longer than 3.5 days. breezes. A large amount of energy is present at the low‐frequency part of the spectrum whose periods These frequencies corresponded to the time scale of synoptic weather patterns. At low frequency range, are longer than 3.5 days. These frequencies corresponded to the time scale of synoptic weather the major wind velocity component exhibited several peaks at periods 3.5, 5.2, 9.7, 13.3, 28, and 62 days. patterns. At low frequency range, the major wind velocity component exhibited several peaks at The minor wind velocity component also has the same energy level in low frequency band to the major periods 3.5, 5.2, 9.7, 13.3, 28, and 62 days. The minor wind velocity component also has the same wind component. energy level in low frequency band to the major wind component.

J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20202020, ,88, ,x 285 FOR PEER REVIEW 66 of of 16 16 /Hz) 2 /Hz) 2 Spectral Density of (m MSLP Spectral Density Spectral Density of wind velocity (m of wind velocity Spectral Density

(a) (b)

1014 108

24h

1012 12h 6 8h 10

1010 6h

62d 4.8h 28d 104 108 4h 13.3d 3h 9.7 d 6 10 5.2d 102 3.5d

104 10-9 10-8 10-7 10-6 10-5 10-4 10-3 Frequency (Hz)

(c) (d) /Hz) 2 /Hz) 2 Spectral of (m Density MSLP Spectral (m of Density wind velocity

(e) (f)

FigureFigure 4. 4. SpectralSpectral energy energy plot plot of of wind wind speed speed components components (major (major component: component: red, red, minor minor component: component: green)green) and and MSLP MSLP (blue (blue color) color) at at ( (aa)) Deylam Deylam station; station; ( (bb)) Bushehr Bushehr station; station; ( (cc)) Lavar Lavar station; station; ( (dd)) Kangan Kangan station;station; ( (ee)) Javad Javad al al-Aemmeh‐Aemmeh station; station; ( (ff)) Bostaneh station.

Similarly,Similarly, the same energy peaks at 12 and and 24 24 h h could could be be detected detected in in the the spectrum spectrum of of MSLP MSLP data. data. ThereThere were also other peaks peaks at at 3, 3, 3.4, 3.4, 4, 4, 4.8, 4.8, 6, 6, and 8 8 h. The The low low-frequency‐frequency peaks peaks were were present present at at 5.2, 5.2, 9.7,9.7, 11.9, 11.9, 28, 28, 43.5, 43.5, and and 76 days. SpectralSpectral analysis analysis on on sea sea-level‐level records records has shown shown that the the main main amount amount of of energy energy in in these these spectra spectra areare concentrated at at low frequencies, and and it it rapidly decreased moving toward higher frequencies (Figure(Figure 55).). TheThe diurnaldiurnal and and semi-diurnal semi‐diurnal signals signals could could be be detected detected by by two two sharp sharp peaks peaks at at 24 24 and and 12 12 h, h,respectively, respectively, Therefore, Therefore, the tidethe tide is the is most the most important important phenomenon phenomenon affecting affecting water levelwater of level the Persian of the PersianGulf. The Gulf. other The peaks other belong peaks belong to shorter to shorter period period harmonics harmonics at 3, 4, at 5, 3, 6, 4, and 5, 6, 8 and h. Tidal 8 h. Tidal range range at these at thesestations stations is between is between 1.8 m at 1.8 Javad m at al-Aemmeh Javad al‐Aemmeh station andstation 3.4 mand at Deylam3.4 m at station.Deylam Also, station. low-frequency Also, low‐ frequencypeaks at 3.5, peaks 5.5, 11,at 3.5, 14, 5.5, 28, and11, 14, 50 days28, and were 50 observeddays were at observed different at stations. different The stations. relative The broad relative peak broadcentered peak at 24centered h could at be 24 due h could to the be interference due to the ofinterference diurnal tidal of diurnal signals and tidal other signals waves and in other the Persian waves inGulf. the ThePersian period Gulf. of The period as a potential of seiche reason as a for potential aforementioned reason for peak aforementioned can be calculated peak according can be calculatedto Merian’s according formula [to22 Merian’s,23]: formula [22,23]:

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2L Tn (3) n2LgH Tn = p (3) n gH where n = 1, 2, 3, … are different modes of oscillation, T is the natural period of a closed basin, L is thewhere length, n = 1,H 2,is 3,the... averageare diff deptherent modes of the ofbody oscillation, of water, T and is the g naturalis the acceleration period of a due closed to gravity. basin, L Consideringis the length, length H is theof the average basin to depth be 820 of km the and body average of water, depth and of g 32.3 is the m, accelerationthe principal due seiche to gravity.period ofConsidering this basin would length be of the25.6 basin h. To to compare be 820 km this and period average with depth the peaks of 32.3 of m, the the sea principal‐level energy seiche spectra, period theof this spectra basin of would Kangan be station, 25.6 h. Towhich compare has the this longest period sea with‐level the record, peaks of was the calculated sea-level energy again using spectra, a smallerthe spectra bandwidth of Kangan (Figure station, 6). It which is shown has the that longest there is sea-level a separate record, peak was around calculated 25.6 h again that may using be a attributedsmaller bandwidth to the mode (Figure 1 seiche6). oscillation It is shown in that the therePersian is Gulf. a separate Indeed, peak it seems around that 25.6 in the h that calculation may be ofattributed seiche period, to the modethe Persian 1 seiche Gulf oscillation acts more in the as a Persian closed Gulf. basin Indeed, (entrance it seems width that smaller in the than calculation the Gulf of width).seiche period, the Persian Gulf acts more as a closed basin (entrance width smaller than the Gulf width).

(a) (b) /Hz) 2 Spectral Density (m Density Spectral

(c) (d)

(e) (f)

FigureFigure 5. 5. EnergyEnergy spectrum spectrum of of sea sea level level at at(a) ( aDeylam) Deylam station; station; (b) (Bushehrb) Bushehr station; station; (c) Lavar (c) Lavar station; station; (d) Kangan(d) Kangan station; station; (e) Javad (e) Javad al‐Aemmeh al-Aemmeh station; station; (f) Bostaneh (f) Bostaneh station. station.

J. Mar. Sci. Eng. 2020, 8, 285 8 of 16 J.J. Mar.Mar. Sci.Sci. Eng.Eng. 20202020,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 1616

Figure 6. Energy spectrum of sea level at Kangan station. Figure 6. Energy spectrum of sea level at Kangan station.

3.2.3.2. CharacteristicsCharacteristics ofof thethe TideTide ToTo extractextractextract harmonic harmonicharmonic coe coefficientscoefficientsfficients from fromfrom the measurement thethe measurementmeasurement data, the data,data, harmonic thethe harmonicharmonic analysis was analysisanalysis performed waswas ® ® performedbyperformed using UTIDE byby using MATLABusing UTIDEUTIDEfunctions MATLABMATLAB (version® functionsfunctions R2017b) (The(version(version Mathworks, R2017b)R2017b) Inc.: (The(The Natick, Mathworks,Mathworks, MA, USA) Inc.:Inc.: [24]. Massachusetts,ThisMassachusetts, analysis describes MA,MA, USA)USA) the [24].[24]. changing ThisThis analysisanalysis elevation describesdescribes of sea the surfacethe changingchanging as a sum elevationelevation of a finite ofof seasea number surfacesurface of asas cosineaa sumsum ofwavesof aa finitefinite with numbernumber specific of propertiesof cosinecosine waveswaves such as withwith amplitudes, specificspecific frequencies,propertiesproperties suchsuch and phases.asas amplitudes,amplitudes, The frequencies frequencies,frequencies, are given andand phases.aphases. priori TheThe and frequenciesfrequencies the other two areare parameters givengiven aa prioripriori will andand be calculated thethe otherother twotwo using parametersparameters least square willwill method. bebe calculatedcalculated The 8 usingusing main least tidalleast squareharmonicssquare method.method. at each TheThe station 88 mainmain are tidaltidal listed harmonicsharmonics in Figure atat7 . eacheach Depending stationstation areare on thelistedlisted length inin FigureFigure of records 7.7. DependingDepending in each station, onon thethe lengthdilengthfferent ofof records diurnal,records inin semi-diurnal, eacheach station,station, differentdifferent and several diurnal,diurnal, ter-diurnal semisemi‐‐diurnal,diurnal, and quarter-diurnal andand severalseveral terter tidal‐‐diurnaldiurnal components andand quarterquarter are‐‐ diurnalresolved.diurnal tidaltidal Due componentscomponents to short sea-level areare resolved.resolved. records DueDue at Lavar toto shortshort and seasea Javad‐‐levellevel al-Aemmeh, recordsrecords atat LavarLavar some constituents, andand JavadJavad alal‐‐ P1Aemmeh,Aemmeh, and K2, someweresome notconstituents,constituents, resolved by P1P1 this andand analysis. K2,K2, werewere notnot resolvedresolved byby thisthis analysis.analysis.

FigureFigure 7. 7. AmplitudeAmplitude ofof thethe mainmain tidaltidal constituentsconstituents in in all all stations. stations.

TheThe principal principal lunar lunar semi semi-diurnal,‐diurnal, M M22, ,harmonic harmonic constituent constituent has has the the largest largest amplitude amplitude in in all all The principal lunar semi‐diurnal, M2, harmonic constituent has the largest amplitude in all stationsstations and and the the other other three three main constituents are K1,,O O11,, and and S S22, ,respectively. respectively. The The tidal tidal from from number number stations and the other three main constituents are K1, O1, and S2, respectively. The tidal from number (FN)(FN) isis calculatedcalculated forfor eacheach station.station. ItIt isis thethe ratioratio ofof thethe sumsum ofof thethe amplitudesamplitudes ofof thethe mainmain diurnaldiurnal harmonic constituents (O1 and K1) to the sum of the main semi‐diurnal constituents (M2 and S2), harmonic constituents (O1 and K1) to the sum of the main semi‐diurnal constituents (M2 and S2),

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 16 (FN) is calculated for each station. It is the ratio of the sum of the amplitudes of the main diurnal Equation (4). As the FN at all stations was between 0.45 and 1.1, the northern coasts of the Persian harmonic constituents (O1 and K1) to the sum of the main semi-diurnal constituents (M2 and S2),

GulfEquation has a (4). mixed, As the predominantly, FN at all stations semi was‐diurnal between tidal 0.45 cycle and [1]. 1.1, the northern coasts of the Persian Gulf has a mixed, predominantly, semi-diurnal tidal cycleK1 [O1].1 FN (4) M2S2 K + O FN = 1 1 (4) M2 + S2 4. Discussion 4. Discussion 4.1. Wavelet Analysis 4.1. Wavelet Analysis As the Fourier Transform only revealed frequencies present in the whole time series, information on individualAs the Fourier events Transform are lost [25]. only However, revealed frequencies the Wavelet present transform in the (WT) whole expands time series, time information series into timeon individual‐frequency events space areand lost can [therefore25]. However, find localized the Wavelet intermittent transform periodicities (WT) expands [26]. time series into time-frequencyThe time‐frequency space and spectrum can therefore of WT find [27] localized is used in intermittent this study to periodicities understand [26 the]. spectral feature and theThe stability time-frequency of the various spectrum frequency of WT [27 processes] is used in in this the study sea‐level to understand records (Equation the spectral (5)). feature This equationand the stability shows ofthe the WT, various which frequency is used processesto analyze in time the sea-level series that records contain (Equation nonstationary (5)). This power equation at manyshows different the WT, frequencies. which is used to analyze time series that contain nonstationary power at many different frequencies. ‐1⁄ 4 iω η ‐γ2⁄2 ψ ηπ e 0 e 2 (5) 0 1/4 iω0η γ /2 ψ0(η) = π− e e− (5) where ψ0 denotes wavelet function, γ is the non‐dimensional time parameter, i is the imaginary where ψ0 denotes wavelet function, γ is the non-dimensional time parameter, i is the imaginary unit unit number, and ω is the non‐dimensional frequency. Typical results from WT are presented for number, and ω is the non-dimensional frequency. Typical results from WT are presented for Bushehr Bushehr (Figure0 8). Both the magnitude and periods of the various frequency signals in the sea level (Figure8). Both the magnitude and periods of the various frequency signals in the sea level can be seen can be seen from the time‐frequency spectrum. Analyses such as this were carried out for all stations, from the time-frequency spectrum. Analyses such as this were carried out for all stations, except for except for Lavar and Javad al‐Aemmeh whose sea‐level records were short to make analysis possible. Lavar and Javad al-Aemmeh whose sea-level records were short to make analysis possible. The results The results show that a large amount of energy is concentrated at tidal frequencies. The neap and show that a large amount of energy is concentrated at tidal frequencies. The neap and spring periods spring periods could be observed clearly in this figure at periods between 12 and 24 h. It is interesting could be observed clearly in this figure at periods between 12 and 24 h. It is interesting that there are that there are phase lags between energy peaks at diurnal and semi‐diurnal harmonics. phase lags between energy peaks at diurnal and semi-diurnal harmonics.

(a)

(b)

Figure 8. TypicalTypical results of wavelet analysis on sea sea-level‐level records at Bushehr station ( a)) Time series of sea level and ( b) Wavelet analysis.

The wavelet analysis of MSLP indicated that these fluctuations were strongest during the autumn and winter regimes (September–February) and occurred preferentially at times scales 9–35

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J. Mar.The Sci. waveletEng. 2020, analysis8, x FOR PEER of MSLP REVIEW indicated that these fluctuations were strongest during the autumn10 of 16 and winter regimes (September–February) and occurred preferentially at times scales 9–35 days. days. Correspondingly, there were lower fluctuations during spring and summer seasons. Diurnal Correspondingly, there were lower fluctuations during spring and summer seasons. Diurnal and and semi‐diurnal energy associated with the sea‐land breeze were clearly recognizable in the wavelet semi-diurnal energy associated with the sea-land breeze were clearly recognizable in the wavelet diagram of minor wind velocity component (Figure 9a). diagram of minor wind velocity component (Figure9a).

(a)

(b)

(c)

FigureFigure 9. 9. TypicalTypical resultsresults of wavelet analysis on on ( (aa)) the the meteorological meteorological parameters parameters including including MSLP, MSLP, (b(b)) Major Major wind wind velocity velocity component, component, and and (c) minor(c) minor wind wind velocity velocity component component (bottom) (bottom) for Bushehr for Bushehr station. station. 4.2. Low-Pass Filtering 4.2. LowTo assess‐Pass Filtering the relation between low-frequency sea-level variation and atmospheric forces, the high frequencyTo assess signals the were relation filtered between from low the‐ observedfrequency sea-level sea‐level data. variation The cutoand ffatmosphericfrequency (half-powerforces, the point)high frequency used in this signals analysis were was filtered 48 h. The from range the ofobserved low-pass-filtered sea‐level data. sea-level The records cutoff frequency was not the (half same‐ alongpower the point) northern used in coasts this analysis of the Persian was 48 Gulf. h. The There range range of low was‐pass higher‐filtered along sea‐ thelevel northwestern records was not part comparedthe same toalong northeastern the northern regions coasts (Figure of 10 the). The Persian variations Gulf. in There non-tidal range sea was level higher at Bushehr along station the werenorthwestern up to 0.75 part m while compared they were to northeastern ~0.60 cm and regions ~0.40 (Figure m at Kangan 10). The and variations Bostaneh in stations, non‐tidal respectively. sea level Also,at Bushehr the seasonal station variationwere up to in 0.75 sea m level while was they detected were ~0.60 using cm 90-day and ~0.40 low-pass m at Kangan filter on and the Bostaneh sea level records.stations, The respectively. highest mean Also, sea-level the seasonal occurred variation during in sea the level summer was months detected (July using to 90 August),‐day low and‐pass the lowestfilter on during the sea winter level records. months (JanuaryThe highest to February).mean sea‐level The occurred difference during in mean the sea-level summer months elevation (July was to August), and the lowest during winter months (January to February). The difference in mean sea‐ level elevation was between 0.20 and 0.25 m. One of the major component of this seasonal sea‐level

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J.J. Mar. Mar. Sci. Sci. Eng. Eng. 2020 2020, ,8 8, ,x x FOR FOR PEER PEER REVIEW REVIEW 1111 of of 16 16 between 0.20 and 0.25 m. One of the major component of this seasonal sea-level fluctuation is the steric fluctuationefluctuationffect [2,28 ]is is caused the the steric steric by seasonaleffect effect [2,28] [2,28] variation caused caused in by by air seasonal seasonal and sea variation heatvariation fluxes. in in air Beyondair and and sea sea this heat heat effect, fluxes. fluxes. the seasonalBeyond Beyond thisvariationthis effect, effect, in the the air seasonal seasonal pressure variation variation may increase in in air air the pressure pressure sea-level may may variations. increase increase the the sea sea‐‐levellevel variations. variations.

FigureFigure 10. 10. Low LowLow-pass-filtered‐pass‐pass‐filtered‐filtered sea sea-levelsea‐level‐level records records at at Bushehr, Bushehr, Kangan, Kangan,Kangan, and andand Bostaneh BostanehBostaneh stations. stations.stations.

The same low-pass filter was been applied to the wind velocity components and MSLP data. TheThe samesame lowlow‐‐passpass filterfilter waswas beenbeen appliedapplied toto thethe windwind velocityvelocity componentscomponents andand MSLPMSLP data.data. Time series of low-pass-filtered records at Bushehr station between February and June 2009 indicated TimeTime series series of of low low‐‐passpass‐‐filteredfiltered records records at at Bushehr Bushehr station station between between February February and and June June 2009 2009 indicated indicated that high sea-level events corresponded to low pressure and onshore wind (Figure 11). Although the thatthat high high sea sea‐‐levellevel events events corresponded corresponded to to low low pressure pressure and and onshore onshore wind wind (Figure (Figure 11). 11). Although Although the the signals agreed well in many of the events, there were significant events where the sea level had signalssignals agreed agreed well well in in many many of of the the events, events, there there were were significant significant events events where where the the sea sea level level had had larger larger larger amplitude fluctuations than atmospheric pressure (mid-February) and vice versa (mid-March). amplitudeamplitude fluctuations fluctuations than than atmospheric atmospheric pressure pressure (mid (mid‐‐February)February) and and vice vice versa versa (mid (mid‐‐March).March). These These These differences were also present in the comparison between wind velocity and sea-level time series. differencesdifferences were were also also present present in in the the comparison comparison between between wind wind velocity velocity and and sea sea‐‐levellevel time time series. series. It It is is It is not always possible to quantify the exact contribution of wind and MSLP to the total non-tidal notnot always always possible possible to to quantify quantify the the exact exact contribution contribution of of wind wind and and MSLP MSLP to to the the total total non non‐‐tidaltidal sea sea‐‐ sea-level fluctuation, because the wind is highly correlated with the gradient of MSLP, and both of them levellevel fluctuation, fluctuation, because because the the wind wind is is highly highly correlated correlated with with the the gradient gradient of of MSLP, MSLP, and and both both of of them them are related to the larger scale atmospheric formations. To quantify the correlation between sea-level areare related related to to the the larger larger scale scale atmospheric atmospheric formations. formations. To To quantify quantify the the correlation correlation between between sea sea‐‐levellevel variation and meteorological forcing, correlation coefficients between these parameters were calculated variationvariation andand meteorologicalmeteorological forcing,forcing, correlationcorrelation coefficientscoefficients betweenbetween thesethese parametersparameters werewere using a moving window of 10 days. The variation of the correlation coefficient with time is shown in calculatedcalculated using using a a moving moving window window of of 10 10 days. days. The The variation variation of of the the correlation correlation coefficient coefficient with with time time Figure 12. The positive unity implies that MSLP and major wind speed component fully explain the isis shown shown in in Figure Figure 12. 12. The The positive positive unity unity implies implies that that MSLP MSLP and and major major wind wind speed speed component component fully fully sea-level response, while the negative unity indicates the reverse behavior. explainexplain the the sea sea‐‐levellevel response, response, while while the the negative negative unity unity indicates indicates the the reverse reverse behavior. behavior.

((aa))

((bb))

FigureFigureFigure 11. 11.11. Low Low-pass-filteredLow‐pass‐pass‐filtered‐filtered time time series series of of sea sea level level compared compared with with ( a (a) )MSLP, MSLP, and andand ( (b(bb)) )major majormajor wind windwind velocityvelocityvelocity component componentcomponent at atat Bushehr BushehrBushehr station. station.station.

J. Mar. Sci. Eng. 2020, 8, 285 12 of 16 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 12 of 16

Figure 12.12.Correlation Correlation between between low-pass-filtered low‐pass‐filtered sea-level sea‐ recordslevel records and meteorological and meteorological forcing including forcing includingmajor wind major component wind component (red line) and(red MSLP line) and (blue MSLP line). (blue line).

The wind components contained higher correlation with sea level compared to atmospheric pressure (Figure 1212).). The The red red line, line, correlation between wind wind and sea level, changed with different different seasons. It It had had the the highest highest values values during during late late autumn/early autumn/early winter. It It was seen that during summer and autumn, autumn, the the correlation correlation coefficient coefficient between between MSLP MSLP and and sea level sea level was significantly was significantly less than less unity than indicatingunity indicating that factors that factors other than other barometric than barometric pressure pressure influence influence sea level sea variability. level variability. However, However, during winterduring and winter spring, and spring,the barometric the barometric pressure pressure had the had highest the highest correlation correlation with sea with level. sea level.

4.3. Cross Cross-Correlation‐Correlation between Parameters One of the possible reasons for low and even negative correlation coecoefficientfficient between meteorological forcing and sea level could be the phase lag betweenbetween thesethese parameters.parameters. Therefore, Therefore, crosscross-spectral‐spectral analysisanalysis was was performed performed through through application application of coherence of coherence spectrum spectrum between between time seriestime seriesof sea-level of sea and‐level wind and velocity wind velocity components. components. The same The analysis same wasanalysis also performedwas also performed between time between series timeof sea series level of and sea MSLP. level and Results MSLP. of thisResults analysis of this at analysis Bushehr at station Bushehr are station depicted are in depicted Figures in13 Figures and 14. 13The and frequencies 14. The frequencies with the highest with the coherency highest coherency were extracted were extracted in each station. in each At station. almost, At all almost, stations, all stations,there were there high were coherency high coherency peaks at periodspeaks at corresponding periods corresponding to 2.4, 10.6 to and 2.4, 13.7 10.6 days. and 13.7 There days. were There also weresome also peaks some at periods peaks at 16.8, periods 23.7 and 16.8, 43.3 23.7 days and at 43.3 Kangan days and at Kangan Bushehr and stations. Bushehr The stations. mean phase The mean lag at 6 6 Bushehr station in the frequency band between 1.5 10 and 7.5 10 −6Hz (equal to periods−6 between phase lag at Bushehr station in the frequency band× between− 1.5× × 10− and 7.5 × 10 Hz (equal to 1.5periods and 7.5between days) was1.5 and 125 ◦7.5. This days) indicated was 125°. that This at these indicated periods, that the at atmosphericthese periods, pressure the atmospheric generally pressureleads to sea-level generally fluctuations leads to sea between‐level fluctuations 1 and 6.4 days, between respectively. 1 and 6.4 This days, figure respectively. also shows This that figure there alsowas noshows consistent that there lag betweenwas no consistent atmospheric lag pressure between and atmospheric sea level at pressure lower frequencies. and sea level There at lower were frequencies.both positive There and negative were both phase positive lag values, and negative which meansphase thatlag values, sometimes which the means atmospheric that sometimes pressure theleads atmospheric to sea-level pressure fluctuations, leads and to sea at‐ thelevel other fluctuations, times it lags. and at the other times it lags. The same procedureprocedure was was followed followed for for the the investigation investigation on theon the relation relation between between sea level sea level and wind and windcomponents. components. Cross spectrumCross spectrum of wind of velocity wind velocity components components versus low-frequency versus low‐frequency sea-level recordssea‐level at recordsBushehr at station Bushehr indicated station that indicated there were that there peaks were at periods peaks 3.5, at periods 5.3, 7.6 and3.5, 5.3, 10.1 7.6 days. and The 10.1 same days. peaks The samewere observedpeaks were in theobserved cross spectrum in the cross at other spectrum stations. at other In addition, stations. there In addition, were peaks there at longerwere peaks periods, at longer33.3 and periods, 40.7 days. 33.3 For and periods 40.7 days. between For periods 3 and 13 between days, the 3 and sea level 13 days, in general the sea lagged level in behind general the lagged major behindwind components the major wind by between components 2 and by 10 between days, respectively. 2 and 10 days, It was respectively. also observed It was that also the observed minor wind that thevelocity minor component wind velocity had lower component correlation had with lower sea correlation level compared with tosea the level major compared component. to the The major other component.findings from The the other spectral findings analysis from are: the (a) atspectral almost analysis at all the are: stations (a) at the almost coherence at all between the stations sea level the coherenceand wind was between larger sea than level the coherencyand wind betweenwas larger sea than level the and coherency MSLP; and, between (b) coherency sea level between and MSLP; wind and,velocity (b) coherency components between and sea-level wind velocity fluctuations components decreased and from sea‐ thelevel west fluctuations (Bushehr) decreased to east (Bostaneh). from the westThe coherence (Bushehr) between to east (Bostaneh). atmospheric The pressure coherence and seabetween level wasatmospheric almost the pressure same at and all the sea stations. level was almostThe the coherence same at all for the Bushehr stations. and Kangan station were generally greater than the one of Bostaneh station.The This coherence indicated for thatBushehr for the and two Kangan former station stations, were a larger generally proportion greater of than sea-level the one variation of Bostaneh may station. This indicated that for the two former stations, a larger proportion of sea‐level variation may be explained by meteorological forces than for the Bostaneh station, which is located at the eastern section of Persian Gulf.

J. Mar. Sci. Eng. 2020, 8, 285 13 of 16

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 16 beJ. Mar. explained Sci. Eng. 2020 by, meteorological 8, x FOR PEER REVIEW forces than for the Bostaneh station, which is located at the eastern13 of 16 section of Persian Gulf.

(a) (a)

(b) (b) Figure 13. Cross spectrum of low‐frequency sea‐level records and MSLP at Bushehr station (a) FigureFigurecoherence 13.13. Cross (bCross) phase spectrum spectrum difference. of low-frequencyof low‐frequency sea-level sea‐level records records and MSLP and atMSLP Bushehr at stationBushehr (a )station coherence (a) (coherenceb) phase di (bff)erence. phase difference.

(a) (a)

(b) (b) FigureFigure 14. 14.Cross Cross spectrum spectrum of low-frequencyof low‐frequency sea-level sea‐level records records and wind and velocity wind velocity components components at Bushehr at stationFigureBushehr (14.a )station coherence Cross (a spectrum) coherence (b) phase of ( di blow)ff phaseerence.‐frequency difference. sea‐ level records and wind velocity components at Bushehr station (a) coherence (b) phase difference. TimeTime seriesseries ofof low-pass-filteredlow‐pass‐filtered sea-levelsea‐level recordsrecords atat Bushehr,Bushehr, Kangan, Kangan, and and Bostaneh Bostaneh tidetide gaugegauge stationsstationsTime overover series aa two-monthtwo of ‐lowmonth‐pass periodperiod‐filtered indicatedindicated sea‐level thatthat records thethe variabilityvariability at Bushehr, at Bushehr Kangan, and and Kangan Bostaneh were tide similar, gauge evenstationseven forfor over lowlow amplitudeaamplitude two‐month fluctuationsfluctuations period indicated (Figure(Figure that 1515).). the However,However, variability atat at Bushehr,Bushehr, Bushehr thethe and amplitudeamplitude Kangan were ofof non-tidalnon similar,‐tidal sea-levelevensea‐level for fluctuation,lowfluctuation, amplitude inin general, general,fluctuations exceededexceeded (Figure thosethose 15). atat However, KanganKangan and andat Bushehr, BostanehBostaneh the stations,stations, amplitude bothboth foroffor non positivepositive‐tidal seaand‐level negative fluctuation, events. Highin general, water ‐exceededlevel conditions those at at KanganBushehr and station Bostaneh generally stations, led to both those for of positiveKangan and negativeBostaneh events. stations. High The water same‐ levelbehavior conditions was observed at Bushehr for lowstation water generally levels (Figureled to those 15). of Kangan and Bostaneh stations. The same behavior was observed for low water levels (Figure 15).

J. Mar. Sci. Eng. 2020, 8, 285 14 of 16 and negative events. High water-level conditions at Bushehr station generally led to those of Kangan J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 16 and Bostaneh stations. The same behavior was observed for low water levels (Figure 15). ThisThis sequence sequence of of high high water water-level‐level occurrence at all stations stations indicated a west to to east east wave wave moving moving alongalong the the northern coasts coasts of of the Persian Gulf. This This wave wave may may be be considered considered to to be be a coastal trapped wave, butbut itit actually actually has has di ffdifferenterent origin. origin. A coastal A coastal trapped trapped waves waves is defined is defined as a wave as a traveling wave traveling parallel parallelto the coast, to the with coast, the with highest the heighthighest at height the shoreline at the shoreline and decreasing and decreasing height off heightshore [offshore7]. In the [7]. northern In the northernhemisphere hemisphere it has to travelit has counterclockwise,to travel counterclockwise, traveling traveling with the coastwith tothe the coast right to [the2,29 right]. However, [2,29]. However,according toaccording above analysis, to above a clockwise analysis, wavea clockwise was observed wave was during observed the complete during studythe complete period. Hence,study period.these low-frequency Hence, these water-levellow‐frequency fluctuations water‐level cannot fluctuations be classified cannot as a be coastal classified trapped as a wave. coastal They trapped were wave.generated They by were the passagegenerated of by atmospheric the passage pressure of atmospheric systems overpressure the Persiansystems Gulf. over the Persian Gulf. ToTo extract the lag lag between between these these time time series, series, a a cross cross-correlation‐correlation analysis analysis was was undertaken undertaken between between eacheach pair pair of of time time series. series. In Inthis this manner, manner, similarity similarity between between the reference the reference time time series, series, i.e., Bushehr i.e., Bushehr low‐ passlow-pass-filtered‐filtered sea‐level sea-level records, records, and and the the shifted shifted (lagged) (lagged) time time series series of of low low-pass-filtered‐pass‐filtered sea sea-level‐level recordsrecords of anotheranother stationstation was was measured measured by by the the cross-correlation. cross‐correlation. The The results results showed showed that that the the mean mean lag lagbetween between the the low-pass-filtered low‐pass‐filtered sea-level sea‐level record record at Bushehr at Bushehr and atand Kangan at Kangan station station was 5.5 was h. 5.5 The h. mean The meanlag between lag between low-pass low sea-level‐pass sea‐ recordslevel records at Kangan at Kangan and Bostaneh and Bostaneh stations stations was 5 was h. The 5 h. dominant The dominant wind windregime regime of the Persianof the Persian Gulf travels Gulf fromtravels the from northwest the northwest towards the towards Strait ofthe Hormuz Strait of and Hormuz matches and the matchessequence the of highsequence/low non-tidalof high/low sea-level non‐tidal occurrences sea‐level asoccurrences described as above. described above.

FigureFigure 15. 15. LowLow-pass-filtered‐pass‐filtered sea sea-level‐level records records at at Bushehr Bushehr (Blue), (Blue), Kangan Kangan (Green), (Green), and and Bostaneh Bostaneh (Red) (Red) stations.stations. The The dashed dashed and and solid solid black black lines lines show show the the sequences sequences of of high high and and low low waters, respectively.

AA longer continuouscontinuous timetime series series of of sea-level sea‐level records records may may be be required required to studyto study the the semi-annual semi‐annual and andannual annual tidal tidal constituents constituents and lower and lower frequency frequency SLV in SLV the Persianin the Persian Gulf. Also, Gulf. it Also, is suggested it is suggested to employ to employsea-level sea data‐level from data the southernfrom the coasts southern of the coasts Persian of Gulf the toPersian better investigateGulf to better the counterclockwise investigate the counterclockwisemovement of non-tidal movement wave of in non the‐ region.tidal wave in the region.

5.5. Conclusions Conclusions TheThe low low-frequency‐frequency sea sea-level‐level variabilities variabilities along along the the northern northern coasts coasts of of the the Persian Persian Gulf Gulf were examinedexamined together together with with the the response response of of sea sea level level to to low low-frequency‐frequency wind wind components components and and MSLP. MSLP. SpectralSpectral analysis analysis revealed revealed that that tides tides were were responsible responsible for formost most of the of spectral the spectral energy energy at sea atlevel. sea level. Harmonic analysis on sea-level records indicated that the principal lunar semi-diurnal, M , Harmonic analysis on sea‐level records indicated that the principal lunar semi‐diurnal, M2, and2 and harmonic constituent had the largest amplitude followed by the other three main constituents harmonic constituent had the largest amplitude followed by the other three main constituents K1, O1, K ,O , and S . Low-pass-filtered sea-level data had a maximum amplitude of 0.75 m at Bushehr and1 S21. Low‐pass2 ‐filtered sea‐level data had a maximum amplitude of 0.75 m at Bushehr station, whichstation, comprised which comprised a significant a significant portion portionof total of sea total‐level sea-level fluctuations. fluctuations. Spectral Spectral analysis analysis on wind on componentswind components and MSLP and indicated MSLP indicated that there that were there energy were peaks energy at peaks periods at periodsfrom 3 days from to 3 2 days months. to 2 Energymonths. peaks Energy at similar peaks at periods similar were periods also were observed also observed in the sea in‐level the sea-leveltime series. time Coherency series. Coherency between lowbetween‐frequency low-frequency sea‐level sea-level records records and MSLP and MSLPindicated indicated that thatfor periods for periods between between 1.5 1.5 and and 7.5 7.5 days, days, atmosphericatmospheric pressure pressure led led to to sea sea-level‐level fluctuations fluctuations at at time time periods periods between between 1 1 and and 6.4 6.4 days. days. Similarly, Similarly, thethe sea level usually laggedlagged upup toto 1010 daysdays behind behind the the major major wind wind velocity velocity component component in in the the range range of of 3- 3‐ to 13‐day periods. The contribution of wind velocity components to the sea‐level fluctuations was higher compared to the effect of atmospheric pressure.

Author Contributions: Methodology, N.A., M.N. and C.P.; software, M.N.; resources, N.A.; data curation, M.N.; writing—original draft preparation, N.A., M.N.; writing—review and editing, N.A., M.N. and C.P.;

J. Mar. Sci. Eng. 2020, 8, 285 15 of 16 to 13-day periods. The contribution of wind velocity components to the sea-level fluctuations was higher compared to the effect of atmospheric pressure.

Author Contributions: Methodology, N.A.-K., M.N. and C.P.; software, M.N.; resources, N.A.-K.; data curation, M.N.; writing—original draft preparation, N.A.-K., M.N.; writing—review and editing, N.A.-K., M.N. and C.P.; visualization, M.N.; supervision, C.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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