Numerical Modelling of the Effects of the Gulf Stream on the Wave Characteristics - MDPI

Journal of
 Marine Science
 and Engineering

Article
Numerical Modelling of the Effects of the Gulf Stream on the
Wave Characteristics
Sonia Ponce de León and C. Guedes Soares *

 Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico,
 Universidade de Lisboa, 1049-001 Lisbon, Portugal; sonia.poncedeleon@centec.tecnico.ulisboa.pt
 * Correspondence: c.guedes.soares@centec.tecnico.ulisboa.pt

 Abstract: The influence of the Gulf Stream on the wind wave characteristics is investigated. Wave-current
 interaction inside the current field can result in significant inhomogeneities of the wave field that
 change the wave spectrum and wave statistics. This study relies on regional realistic simulations
 using high resolution in time, space and in the spectral space that allow to solve small scale features
 of the order of 5 km. Wave model simulations are performed with and without ocean currents to
 understand the impact of the Gulf Stream. Modelled wave spectra are examined along the main axis
 of the Gulf Stream, and also along a transect that crosses the current. The behavior of significant
 wave height (Hs), the current speed, as well as the mean wave propagation and the current direction
 are analyzed at the selected transect locations. It is shown that inside the current the spectral wave
 energy grows if the wave and the current are aligned and opposed which result in a very peaked
 and elongated spectrum. The Gulf Stream causes a widening of the spectrum angular distribution.
 The results indicate that the Hs increases with the current velocity once the waves are inside the
 Gulf Stream. Most of the time, waves travelled in opposite direction to the current that flows from
 the SW to the NE, which could explain why inside the Gulf Stream waves are high. The validation
 of the numerical simulations is performed for Hs using different wave buoy data available in the
 study region for the winter period of 2019. In addition, one-dimensional wave spectra measured by
 


 an NDBC (National Data Buoy Center) wave buoy are compared with the WAM (Wave Advanced
 

 Modeling) modelled 1d spectra showing a good correlation. Accounting for ocean currents improves
Citation: Ponce de León, S.; Guedes the quality of the simulated results, which is more realistic than only considering waves.
Soares, C. Numerical Modelling of
the Effects of the Gulf Stream on the
 Keywords: Gulf Stream; wave–current interaction; WAM model; influence of current on wind waves;
Wave Characteristics. J. Mar. Sci. Eng.
 NDBC wave buoy spectra; extreme waves
2021, 9, 42. https://doi.org/10.3390/
jmse9010042

Received: 9 December 2020
Accepted: 29 December 2020
 1. Introduction
Published: 4 January 2021 The Gulf Stream is an extraordinary boundary current along the eastern U.S. coast that
 carries large amounts of heat poleward across the North Atlantic, ensuring a warm climate
Publisher’s Note: MDPI stays neu- in Europe. The Gulf Stream is the prototype of the classical western boundary current [1].
tral with regard to jurisdictional clai- The stream mean path along the east coast is driven by a combination of boundary form,
ms in published maps and institutio- bottom topography, entrainment of fluid from the inner gyre and the adjustment of the
nal affiliations. current to the increase in planetary vorticity as fluid move to the North [2]. The meandering
 behavior of the Gulf Stream as well as the creation of border eddies and its attendant warm
 plumes is extensively documented and observed [3].
Copyright: © 2021 by the authors. Li-
 The Gulf Stream fluctuates like a river through the Straits of Florida bordering the U.S.
censee MDPI, Basel, Switzerland.
 coast until it deviates northward from the slope at Cape Hatteras. Some studies describe
This article is an open access article
 the Gulf Stream and its particular behavior of interacting with the local topography [4,5].
distributed under the terms and con- Large meanders and frontal eddies are observable on the inshore side of the Gulf Stream,
ditions of the Creative Commons At- with cyclonic eddies circulating along the shelf. The Gulf Stream eddies occur where the
tribution (CC BY) license (https:// Gulf Stream interacts with the slope and shelf [6].
creativecommons.org/licenses/by/ Wave–current interaction (or the effect of current on waves) can produce steep waves
4.0/). when waves face an opposing current as has been demonstrated in several experimental

J. Mar. Sci. Eng. 2021, 9, 42. https://doi.org/10.3390/jmse9010042 https://www.mdpi.com/journal/jmse

J. Mar. Sci. Eng. 2021, 9, 42 2 of 15

 studies. The basic formulations of wave–current interaction have been verified experimen-
 tally in wave flumes [7–9]. Nwogu [10] has conducted laboratory tests in a multi-directional
 wave basin using both regular and irregular waves, with different angles between the
 current and wave fields. He observed that when a wave system is met by a following
 current, the wave spectrum decreases in terms of its energy, and that the opposite happens
 when the current has the opposite direction. Guedes Soares and Pablo [11] also conducted
 a study in an offshore basin, having observed that with opposite current the wave height
 increases, waves become shorter and propagate faster, while exactly the opposite happens
 with following current. Additional experimental studies showed that this interaction be-
 tween waves and currents can lead to the generation of extreme waves [12,13] In addition,
 wave–current interactions increase the wave breaking that is a good visual indicator of the
 effect of currents on waves [14,15].
 To check the performance of a wave model in representing the wave–current interac-
 tion, Rusu, and Guedes Soares [16] have used the SWAN (Simulating Waves Nearshore)
 model [17] to analyze the laboratory data of [11]. The simulations were carried out in the
 stationary mode, which assumes that the time scale of changes in the boundary condition is
 much less than the time of the waves remaining in the computational area. As there was no
 wind, both the wind growth the quadruplet–wave interactions and whitecapping options
 were switched off in SWAN. The triad wave–wave interactions that are characteristic to
 shallow water situations were also switched off. The results showed that the numerical
 model could represent qualitatively the changes induced by currents on wave spectra.
 This model has been further used [18] to study the interaction of waves and (tidal) currents
 at the entrance of the Tagus estuary being able to reproduce the effects although there were
 not detailed measurements to fully validate the results. There have been several studies on
 the wave–current interaction since the 1980s and the majority were based on numerical
 simulations applications in large-scale rings or meandering currents [19–21] and more
 recently a study was made of the situation at the Agulhas current [22,23].
 Later, Wang et al. [24] analyzed measured wave buoy spectra (from the SWADE—
 Surface Wave Dynamics Experiment) inside and outside the Gulf Stream concluding that
 the directional wave measurements show the changes in wave direction, wave energy,
 and directional spreading when waves encountered the current in the Gulf Stream meander.
 The main sources of the variability of the Gulf Stream on significant wave heights at
 scales less than 200 km were discussed by Ardhuin et al. [25], who compared the numerical
 results obtained with WW3 (WaveWatch III) with satellite altimeter tracks.
 Despite the amount of measured information (satellite, wave buoys, ship observations,
 etc.) available on the last few years, the numerical wave modelling community faces the
 big challenge of simulating the complex processes that are involved in the interaction of
 waves and currents. To ensure good results, three main ingredients are needed: robust
 models that include all the relevant physics involved in this process, especially around
 meanders and eddies; high resolution input data such as bathymetry, wind and currents
 and high-resolution simulations.
 The goal of the present study is to model the waves on the Gulf Stream leading to a
 better understanding of the impact of the Gulf Stream on the wave characteristics. A third-
 generation wave model is applied to a regional nested grid to analyze modelled wave
 spectra with high spectral resolution during the winter of 2019 when waves and the current
 are aligned and when they are opposed. The analysis is made inside the Gulf Stream and
 at adjacent locations.
 The paper is structured as follows: Section 2 presents the wave model set-up and
 the validation of the simulations, together with a short description of the input data.
 The spatial pattern of the mean wave parameters from the simulations with/without
 currents are analyzed in Section 3. In Section 4, the Gulf Stream effect on the wave spectra
 is discussed through a comparison of the wave spectra along the main axis (inside) of the
 Gulf Stream and along a cross section profile (outside). Conclusions and future work are
 given in Section 5.

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 3 of 16

 and along a cross section profile (outside). Conclusions and future work are given in Sec-
J. Mar. Sci. Eng. 2021, 9, 42
 tion 5. 3 of 15

 2. Materials and Methods
 2.1. Wave Model Setup
 2. Materials and Methods
 The configuration of WAM (Wave Advanced Modeling) [26–28] grid model covers
 2.1. Wave Model Setup
 the Gulf Stream region. In this configuration two different grids are implemented: a coarse
 and aThe configuration
 nested of WAM
 high-resolution (Wave
 grid, Advanced
 at spatial Modeling)
 resolution [26–28]
 of 0.125° grid
 and model
 0.05°, covers the
 respectively.
 Gulf Stream region. In this configuration two different grids are implemented:
 Bathymetry grids for all domains are constructed from Etopo1 [29] from the NOAA’s a coarse
 Na-
 and a nested high-resolution grid, at spatial resolution of 0.125 ◦ and 0.05◦ , respectively.
 tional Geophysical Data Centre, with a resolution of 1 min of degree in latitude and lon-
 Bathymetry
 gitude, whichgrids for all domains
 was linearly are constructed
 interpolated to the modelfrom
 grid. Etopo1
 Figure 1[29] from
 shows thethe NOAA’s
 bathymetry
 National Geophysical Data Centre, with a resolution of 1 min of degree
 grids and the distribution of the WAM output locations that coincide with the in latitude and lon-
 wave
 gitude,
 buoys. which was linearly interpolated to the model grid. Figure 1 shows the bathymetry
 grids and the distribution of the WAM output locations that coincide with the wave buoys.

 (a) (b)
 Figure
 Figure 1.
 1. Bathymetry
 Bathymetry grids:
 grids: coarse
 coarse (a)
 (a) and
 and nested
 nested (b);
 (b); locations
 locations of
 of the
 the NDBC
 NDBC wave
 wave buoys
 buoys and WAM outputs.
 and WAM outputs.

 The wave spectrum for the coarse grid configuration is provided for 36 directional directional
 bands measured
 measuredclockwise
 clockwisewith withrespect
 respecttotothethe true
 true north,
 north, andand 38 frequencies
 38 frequencies logarithmi-
 logarithmically
 cally
 spaced spaced
 from from the minimum
 the minimum frequency
 frequency of 0.030
 of 0.030 Hz atHz at intervals
 intervals of Df/fof =Df/f
 0.1.=On
 0.1.the
 Oncase
 the
 case
 of theof high-resolution
 the high-resolution nested
 nested grid grid encompassing
 encompassing thethe GulfStream,
 Gulf Stream,38 38frequencies
 frequencies and
 48 directions are used.
 The open boundaries for the coarse grid model are forced by wave spectra taken from
 the ECMWF (European Centre for Medium-Range Weather Forecasts) Forecasts) ERA5ERA5 (ECMWF
 (ECMWF
 Reanalysis) reanalysis
 reanalysiswave wavemodelmodel (IFS documentation
 (IFS documentation 2019). For the
 2019). Forcoarse and theand
 the coarse nested
 the
 grids shown
 nested in Figure
 grids shown 1, the ERA-5
 in Figure ECMWF
 1, the ERA-5 wind reanalysis
 ECMWF [30] was[30]
 wind reanalysis chosen. More details
 was chosen. More
 about the
 details wave
 about themodel
 wave implementation
 model implementation used can be found
 used can bein Tablein1.Table 1.
 found
 Current effects are considered in the WAM model
 Current effects are considered in the WAM model (see Equation (see Equation (1)).(1)).
 However,
 However, there are
 there
 some difficulties to represent properly all the complex processes that
 are some difficulties to represent properly all the complex processes that are related with are related with
 the wave–current
 the wave–current interactions
 interactions in in the
 the presence
 presence of of strong
 strong currents
 currents such
 such as as Agulhas
 Agulhas or or Gulf
 Gulf
 Stream [31].
 Stream [31]. The
 The most
 most dramatic
 dramatic effects
 effects may
 may be be found
 found when
 when the
 the waves
 waves propagate
 propagate against
 against
 the current.
 the current. For Forsufficiently
 sufficientlylargelargecurrent,
 current, wave
 wave propagation
 propagation is prevented,
 is prevented, andandwavewavere-
 reflection occurs
 flection occurs [32]. [32].
 The evolution
 The evolutionofofthe thetwo-dimensional
 two-dimensional ocean wave
 ocean wavespectrum
 spectrumF (f —frequency,
 F (f—frequency, θ—mean—
 wave propagation direction, with respect
 mean wave propagation direction, -latitude, -longitude) with respect to the frequency
 φ—latitude, λ—longitude) to the frequency and
 direction
 and as a as
 direction function of latitude
 a function andand
 of latitude longitude
 longitudeis governed
 is governedby the transport
 by the Equation
 transport Equation (1).
 The model is formulated in finite differences on regular and rectangular
 (1). The model is formulated in finite differences on regular and rectangular grids. In the grids. In the
 presence of
 presence of currents,
 currents, thethe governing
 governing equation
 equation cancan be
 be written
 written asas
 ∂F 
 ++(Cg ++u )
 ( )·∇∙ F ==Stot
 (1)
 ∂t 
 where u is the current velocity, Cg is the group velocity, t is the time and Stot is the source
 function which considers all the physical processes that allow the growth and the decay
 of waves: the wave energy generation, dissipation, and nonlinear wave–wave interaction.

J. Mar. Sci. Eng. 2021, 9, 42 4 of 15

 The processes included in the model are wave generation by wind [33], nonlinear resonant
 wave–wave interactions ([34], and the whitecapping [35]).

 Table 1. Parameters of the WAM model implementation for Gulf Stream.

 Parameters Coarse Grid Nested Grid
 Simulation period 01/01/2019–28/02/2019
 Geographical domain 58◦ N, 20◦ N, 20◦ W, 85◦ W 42◦ N, 32◦ N, 65◦ W, 80◦ W
 Spatial resolution 0.125 ◦ 0.05◦
 Number of points (521, 305) 158,905 (301, 201) 60,501
 Number of directional bands 36 48
 Number of frequencies 38 38
 Frequency range (Hz) 0.03–1.0201 Hz
 Type of spectral model Deep water
 Propagation Spherical
 Sin + Sdis from WAM cycle 4 (ECMWF WAM) Yes
 Wind input [33]
 Whitecapping dissipation [35]
 Nonlinear interactions [34]
 Current refraction Yes
 Wind input time step (hour) 1
 Wave model output time step (hour) 1
 Integration & source time steps (seconds) 200 90
 Wind data Era-5 reanalysis
 Bathymetry data Etopo 1

 Two independent numerical simulations are performed: with and without ocean
 currents. Current data comes from Mercator Ocean in the framework of the Copernicus
 Marine Environment Monitoring Service (CMEMS). The Operational Mercator global
 ocean analysis-forecast (phy-0010024) is an hourly product with a 1/12◦ of horizontal
 resolution [36]. Mercator Ocean monitoring and forecasting systems have been routinely
 operated in real time since early 2001.

 2.2. Validation
 The validation is performed for the significant wave height (Hs) using wave buoys data
 provided by NDBC (NOAA) (Figure 1) and Environment and Climate Canada. Table 2 shows
 some of the statistical parameters computed. The validation is made for the two hind-
 casts performed: (1) considering only waves (WWav) and (2) including currents (WCur).
 The bias is defined as the difference between the mean observation and the mean predic-
 tion. The scatter index (S.I.) is defined as the standard deviation of the predicted data with
 respect to the best fit line, divided by the mean observations.

 Table 2. Statistics for the Hs. S.I.—Scatter Index; cc-correlation coefficient, n—number of records. Bias, the best-fit scatter
 index and slopes between wave buoys observations and modelled Hs from WAM. Left column-results from simulation
 without current (WWav); Right column-results from simulation considering wave–current interactions (WCur).

 Parameter Location 44137 Location 41046 Location 41047
 Coordinates (latitude, longitude) 42.260◦ N 62◦W 23.822◦ N 68.822◦ W 27.514◦ N 71.494◦ N
 simulation WWav WCur WWav Wcur WWav WCur
 bias 0.06 0.04 0.134 0.095 0.11 0.08
 slope 0.97 0.99 0.918 0.94 0.94 0.95
 S.I. 0.13 0.11 0.123 0.123 0.11 0.11
 RMSE 0.44 0.36 0.253 0.24 0.23 0.22
 cc 0.96 0.98 0.90 0.91 0.94 0.95
 n 1416 1414 1414

was underestimated by the model. In general, the model had the tendency of underesti-
 mate the observations with a positive bias (0.04) (Figure 2, right panel, see Table 2).

 Table
J. Mar. Sci. Eng. 2. Statistics
 2021, 9, 42 for the Hs. S.I.—Scatter Index; cc-correlation coefficient, n—number of records. Bias, the best-fit scatter
 5 of 15
 index and slopes between wave buoys observations and modelled Hs from WAM. Left column-results from simulation
 without current (WWav); Right column-results from simulation considering wave–current interactions (WCur).

 Parameter Location
 The best 44137 coefficientLocation
 correlation found 41046
 corresponds to theLocation 41047
 location 44,137 from the
 Coordinates (latitude,
 simulation considering currents (0.98, case WCur with current) and the
 42.260°N 62°W 23.822°N 68.822°W 27.514°N 71.494°N correlation
 worst
 longitude) was obtained for the wave buoy location (0.90, case WWav only waves). The scatter
 simulation WWav
 indexes varied in theWCur WWav
 range of 0.11 (WWav and Wcur
 WCur) toWWav WCur
 0.13 (location 44137, WWav),
 bias 0.06 0.04 0.134 0.095 0.11 0.08
 whereas the bias varied from 0.05 (44137, WCur) and 0.13 (loc 41046, WWav). The best
 slope 0.97 0.99 0.918 0.94 0.94 0.95
 slope corresponded to the simulation with currents and to the location 44137 (0.99) (Table 2,
 S.I. 0.13 0.11 0.123 0.123 0.11 0.11
 Figure 2). As can be seen, the systematic deviation (bias) is always lower for the case with
 RMSE 0.44 0.36 0.253 0.24 0.23 0.22
 currents compared without currents, the absolute errors, as measured by the RMS error is
 cc 0.96 0.98 0.90 0.91 0.94 0.95
 lower for the simulation with currents, which also improves the dispersion (S.I) and the
 n 1416 1414 1414
 correlation coefficient between the hindcast and the wave buoys measurements.

 (a) (b)
 Figure
 Figure 2. 2. Comparison
 Comparison of the
 of the Hs Hs
 timetime series
 series for wave
 for the the wave
 buoybuoy #44137
 #44137 (a) from
 (a) from the simulation
 the simulation considering
 considering currents
 currents (blue
 (blue line)
 line) and from the wave buoys observations (red line) and the scatter
 and from the wave buoys observations (red line) and the scatter plots (b). plots (b).

 TheUsually,
 comparison the validation of the numerical
 of the modelled and observed simulations is performed
 Hs is depicted by a simple
 in Figure com-
 2a for the
 parison
 best of thesimulation
 correlated typical averaged parameters
 (considering (Hs, mean
 current). As canwave be seendirection),
 a good but very seldom
 correlation was a
 comparison
 obtained for the oflocation
 the wave spectra
 #44137 is given.
 (East Scotia).InDuring
 terms theof thestudyspectral density
 period at leastineight
 this storms
 study, a
 cancomparison
 be identified (fromwith thevalues
 simulation
 higher with
 than currents)
 5 m. The of biggest
 the one-dimensional
 storm with Hswave = 11spectra
 m was is
 presented for the
 underestimated bylocation
 the model. #44014 where 1d
 In general, thewave
 model spectra were
 had the measured
 tendency of during the storm
 underestimate
 theofobservations
 the 25/01/2019 with (Figure 3). This
 a positive comparison
 bias (0.04) (Figure shows
 2b, see that
 Tablein2).general the wave model
 Usually,
 matches thethepeak validation
 frequency, of the
 andnumerical
 the wave simulations
 spectra are of is performed
 the same orderby a of
 simple com-
 magnitude,
 parison
 however, of the typical averaged
 sometimes the modelled parameters
 spectral(Hs,peakmean wave shifted
 is slightly direction), but frequencies
 to high very seldom(at
 a comparison
 08 UTC (Coordinated of the wave spectra Time),
 Universal is given. 10 In
 UTC, terms
 andofatthe 12 spectral
 UTC). density in this study,
 a comparison
 In this case,(from the the simulation
 wave model has with currents)
 less frequenciesof the one-dimensional
 (38) and covers a higherwavefrequency
 spectra
 is range
 presented for the
 (0.03–1.02 Hz) location
 than the #44014
 wavewhere buoys1d (47wave spectra from
 frequencies, were 0.02
 measured during
 Hz to 0.49 Hz).the
 We
 storm of the
 believe it is25/01/2019
 for this reason(Figurethat3).the
 This comparison
 differences shows
 in the that inshapes
 spectral general the wave
 exist. In themodel
 case of
 matches
 the missed the peak
 second frequency, and the
 spectral peak, thewave
 modelspectra
 does not arehave
 of the same order
 sufficient of magnitude,
 resolution to capture
 however, sometimes the modelled spectral peak is slightly
 it and/or the high frequency part components corresponding to local winds are not repro- shifted to high frequencies
 (atduced
 08 UTC (Coordinated
 totally in the Era-5 Universal
 reanalysis Time),
 wind 10fields.
 UTC, and at 12 UTC).
 InInthis case, the wave model has less
 addition, the measured wave spectra at times frequencies (38)
 06,and10,covers
 and 12a UTC
 higherarefrequency
 underesti-
 range
 mated (0.03–1.02
 by the wave Hz) thanmodelthe whereas
 wave buoys (47 frequencies,
 at high frequencies from 0.02 Hz to
 the observed 0.49 spectra
 wave Hz). Weshow be-
 lieve it is forspectral
 secondary this reason peaksthat
 thatthethedifferences
 wave model in the spectral
 cannot shapeswhich
 reproduce, exist. could
 In thebe case of
 associ-
 the missed second spectral peak, the model does not have
 ated with several and different sources of errors of the numerical simulations: errors in sufficient resolution to cap-
 ture it and/or the high frequency part components corresponding to local winds are not
 reproduced totally in the Era-5 reanalysis wind fields.

the wind field, errors in the physical processes represented in the WAM model to cope
 with the wave–current interactions, some of these are: refraction by the current, reflection
 (absent) and wave blocking. The last one, is where waves and currents oppose each other
J. Mar. Sci. Eng. 2021, 9, 42 and stop wave propagation, but the mechanism by which wave energy is removed at 6 ofthe
 15
 blocking point is not understood yet [37].

 (a) (b)

 (c) (d)
 Figure 3.
 Figure 3. Comparison
 Comparison of the 1D wave spectra for the location of the NDBC wave buoy #44014 (Virginia from the simulation
 (Virginia from simulation
 considering currents (blue line) and from the wave buoy observations (red line) for the 25 of January 2019 for 06
 considering currents (blue line) and from the wave buoy observations (red line) for the 25 of January 2019 for 06 UTC UTC (a),
 (a),
 08 UTC (b), 10 UTC (c) and12 UTC (d). Latitude: 36.609°N,
 ◦ Longitude: 74.842°W.
 08 UTC (b), 10 UTC (c) and12 UTC (d). Latitude: 36.609 N, Longitude: 74.842 W. ◦

 3. Results and Discussions
 In addition, the measured wave spectra at times 06, 10, and 12 UTC are underestimated
 by the waveofmodel
 Comparison whereas
 the Spatial at high
 Patterns in frequencies the with
 the Simulations observed wave spectra
 and without show secondary
 Currents
 spectral peaks that the wave model cannot reproduce, which could be associated with
 The MERCATOR current field for the coarse grid can be seen (Figure 4) for the
 several and different sources of errors of the numerical simulations: errors in the wind
 15/01/2019 at 20 UTC showing current speeds higher than 2 m/s and depicting clearly the
 field, errors in the physical processes represented in the WAM model to cope with the
 meandering character of the Gulf Stream propagating from the SW to the NE. The left
 wave–current interactions, some of these are: refraction by the current, reflection (absent)
 middle panel shows the Gulf Stream in the frame of the high-resolution nested grid show-
 and wave blocking. The last one, is where waves and currents oppose each other and stop
 ing with more details the Gulf Stream and the meanders as obtained from the MERCA-
 wave propagation, but the mechanism by which wave energy is removed at the blocking
 TOR ocean current data.
 point is not understood yet [37].

 3. Results and Discussions
 Comparison of the Spatial Patterns in the Simulations with and without Currents
 The MERCATOR current field for the coarse grid can be seen (Figure 4a) for the 15/01/2019
 at 20 UTC showing current speeds higher than 2 m/s and depicting clearly the meandering
 character of the Gulf Stream propagating from the SW to the NE. Figure 4b shows the Gulf
 Stream in the frame of the high-resolution nested grid showing with more details the Gulf
 Stream and the meanders as obtained from the MERCATOR ocean current data.

J. Mar. Sci. Eng. 2021, 9, 42 7 of 15
 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 16

 (a)

 (b) (c)

 (d) (e)
 Figure 4.
 Figure 4. Current
 Current velocity
 velocity field
 field (source:
 (source: MERCATOR
 MERCATOR ocean)
 ocean) from
 from the
 the coarse
 coarse grid
 grid domain
 domain (a),
 (a),the
 thecur-
 current field from the high resolution nested grid (b), the WAM peak period (c), WAM modelled
 rent field from the high resolution nested grid (b), the WAM peak period (c), WAM modelled Hs
 Hs considering currents (d) and the WAM Hs without current (e) for the 15th of January 2019 at 20
 considering currents (d) and the WAM Hs without current (e) for the 15th of January 2019 at 20 UTC.
 UTC.

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 16
 J. Mar. Sci. Eng. 2021, 9, 42 8 of 15

 The peak period (middle right panel) is depicted for the same date showing high
 values above 12 seconds coinciding with the Gulf Stream from the SW side of the grid up
 to the latitude The36°N
 peakand the intrusion
 period (Figure 4c)of is
 thedepicted
 swell offor
 14 the
 seconds
 samepropagating
 date showing from
 highthe NE above
 values
 into the12region of the simulation.
 s coinciding with the GulfA comparison
 Stream from between
 the SWthe side modelled
 of the gridHs up
 is depicted in
 to the latitude 36◦
 the bottom
 N and panels of Figure of
 the intrusion 4 from whichofthe
 the swell 14 clear effect thatfrom
 s propagating has the
 the Gulf Stream
 NE into the in the of the
 region
 wave field can be seen.
 simulation. A comparison between the modelled Hs is depicted in the bottom panels of
 Once the wave
 Figure 4 fromfield
 whichpropagates
 the clear from
 effectthe NE
 that hasinthe
 an opposite
 Gulf Stream direction facingfield
 in the wave the Gulf
 can be seen.
 Stream one of the effects is the increase of the Hs inside the current
 Once the wave field propagates from the NE in an opposite direction facing(bottom left) as ob-the Gulf
 tained from
 Stream theone
 simulation considering
 of the effects the current.
 is the increase of the HsIninside
 this case for the (bottom
 the current 15/01/2019left)atas20obtained
 UTC thefromHs reached the 3 mconsidering
 the simulation and repeatsthe thecurrent.
 shape ofInthe
 thisGulf
 caseStream
 for the itself. The fact
 15 January 2019thatat 20 UTC
 waves propagate in opposite
 the Hs reached the 3 m direction to thethe
 and repeats current
 shapeincreases
 of the Gulf theStream
 Hs. In itself.
 addition,
 Theitfact
 seems
 that waves
 propagate
 that there in opposite
 are not noticeable directioninto
 variations thethe current
 mean waveincreases the Hs.
 propagation In addition,
 directions fromitbothseems that
 compared there are not noticeable
 simulations with/withoutvariations
 current. in the mean wave propagation directions from both
 compared
 From simulations
 the evolution of the with/without current.
 wave field (15/01/2019–16/01/2019) (Figure 5) from the sim-
 From the
 ulation considering evolution
 currents, canofbethe
 seen wave
 (top field (15the
 panels) January 2019–16
 coexistent January
 of mixed wave2019) (Figure 5)
 fields
 of Hs offrom
 3 m the simulation
 covering almost considering
 whole thecurrents, can be seen
 domain together with(top
 thepanels) the coexistent
 high values of the Hs of mixed
 wave
 just in the fieldsof
 location ofthe
 Hs Gulf
 of 3 m covering
 Stream as a almost wholewhich
 fine feather the domain
 vanishes together
 with timewithasthe
 thehigh
 Hs values
 decreasesof down
 the Hsto just
 two in meters
 the location
 on theof16/01/2019
 the Gulf Stream
 (bottomas panels).
 a fine feather which vanishes with time
 as the Hs decreases down to two meters on the 16 January 2019 (bottom panels).

 Figure 5. Evolution of the wave field. Row wise from the top from the 15/01/2019 at 17 UTC up to
 Figure 5. Evolution of the wave field. Row wise from the top from the 15/01/2019 at 17 UTC up to
 16 January 2019 at 14 UTC.
 16/01/2019 at 14 UTC.

 4. Assessment of the Influence of the Gulf Stream on Waves

J. Mar. Sci. Eng. 2021, 9, 42 9 of 15

 4. Assessment of the Influence of the Gulf Stream on Waves
 J. Mar. Sci. Eng. 2020, 8, x FOR PEER 4.1. Analysis of Wave Spectra Along the Main Axis of the Gulf Stream
 REVIEW 10 of 16
 Since the interest is in knowing what the effect of the Gulf Stream on the spectral
 4.1. Analysis of Wave Spectra Along the Main Axis of the Gulf Stream
 shapes is, the objective is to analyze the modelled wave spectra on the current. In this
 Since the interest is in knowing what the effect of the Gulf Stream on the spectral
 regard, hundreds of wave spectra were analyzed along the current axis. The Gulf stream’s
 shapes is, the objective is to analyze the modelled wave spectra on the current. In this
 axis is hundreds
 regard, found byoflooking for the
 wave spectra weregrid nodes
 analyzed with
 along thethe maximum
 current axis. Thecurrent magnitude at each
 Gulf stream’s
 grid
 axis islongitude.
 found by looking for the grid nodes with the maximum current magnitude at each
 Two main cases are analyzed: when waves and the current are opposed and when
 grid longitude.
 waves Two main
 and thecases are analyzed:
 current when
 propagate waves
 with theand the current
 almost sameare opposed and when
 direction.
 waves and the current propagate with the almost same direction.
 4.1.1. Case #1: Waves and Current Opposed
 4.1.1. Case #1: Waves and Current Opposed
 A comparison of the wave spectra from simulations with and without currents for the
 A comparison of the wave spectra from simulations with and without currents for
 dates 1515/01/2019
 the dates January 2019 at 20is UTC
 at 20 UTC shownisinshown
 Figure 6inatFigure
 location6#16at (Figure
 location #16panel).
 6, left (Figure 6a). As can
 be
 As seen
 can bethe
 seenGulf Stream
 the Gulf flows
 Stream flowsalmost stationary
 almost stationary fromfrom
 the the
 SW to SWNEto(top
 NEpanel,
 (Figure 4a), at the
 Figure time
 same 4), at the same propagates
 waves time waves propagates
 to the SW to the SW (bottom
 (Figure left, Figure
 4d) contrary to4)the
 contrary to This natural
 current.
 the current. result
 condition This natural condition
 in certain result in
 spectral certain spectral shapes.
 shapes.

 (a) (b)

 (c) (d)
 Figure 6. The Gulf Stream snapshot (a) showing the position of the wave spectra along the current,
 Figure 6. The Gulf Stream snapshot (a) showing the position of the wave spectra along the current,
 comparison of the 1D WAM wave spectra (b). The 2D WAM total wave spectrum from the simula-
 comparison of the 1D
 tion without currents WAM
 (c) and fromwave spectra (b).
 the simulation The 2Dthe
 considering WAM total
 current (d)wave
 for thespectrum
 date from the simulation
 15/01/2019 at 20 UTC. Lat.: 36.17°N, 73.67°W. Red arrow-wind direction, black arrow-mean wave
 without currents (c) and from the simulation considering the current (d) for the date 15 January 2019
 propagation direction, blue arrow-current direction. Symbols in the bottom of each wave spectra:
 at 20 UTC. Lat.: 36.17◦ N, 73.67◦ W. Red arrow-wind direction, black arrow-mean wave propagation
 direction, blue arrow-current direction. Symbols in the bottom of each wave spectra: ϕ (wind
 direction), θ (wave direction), α (current direction), U (Current velocity). Wave and current direction
 arrows were rotated 180◦ to show following or opposing waves and current. The arrowhead (circle)
 points to where the waves and currents propagate (oceanographic convention).

arrowhead (circle) points to where the waves and currents propagate (oceanographic convention).

 The effect of the Gulf Stream on the spectral wave shape is clear (Figure 6). For the
 1d spectrum (Figure 6, top right panel), the blocking of wave energy due to the opposing
J. Mar. Sci. Eng. 2021, 9, 42 current causes an increase in the spectral peak energy and in the Hs. The 2D spectrum 10 of 15
 without currents (Figure 6 lower left panel) shows higher local energy levels with peak
 spectral energy above 10 m2/Hz/radian and is limited in the 210°–270° sector; however,
 the total spectral energy as measured by the Hs is lower (2.11 m) than the case with cur-
 The effect
 rents (2.83 of the6 lower
 m; Figure Gulf Stream on the In
 right panel). spectral wave
 this case, shape
 while theispeak
 clearenergy
 (Figureis6).lower,
 For the
 the1d
 spectrum (Figure 6b), the blocking of wave energy due to the opposing current
 spectrum is wider, occupying the whole SW sector with high energy levels spread instead causes an increase
 ofinconcentrated
 the spectral peak energy
 in the andpeak
 spectral in theregion.
 Hs. TheThe
 2D effect
 spectrum without
 of the currentcurrents
 on the(Figure
 2D wave 6c)spec-
 shows
 higher local energy levels with peak spectral energy above 10 m 2 /Hz/radian and is limited
 trum is thus to spread the wave energy due to the refraction caused by the current’s spatial
 in the 210◦ –270◦ sector; however, the total spectral energy as measured by the Hs is lower
 gradients.
 (2.11 m) than the case with currents (2.83 m; Figure 6d). In this case, while the peak energy
 is lower,
 4.1.2. Case the spectrum
 #2. Waves andisCurrent
 wider, occupying the whole
 Almost Aligned SW sector
 Propagating with
 to the NEhigh energy levels
 spread instead of concentrated in the spectral peak region. The effect of the current on the
 In the case when waves are almost aligned with the current (from the SW quadrant)
 2D wave spectrum is thus to spread the wave energy due to the refraction caused by the
 and the wind blows from the NE (see the red vector in the wave spectra) the spectral wave
 current’s spatial gradients.
 energy is higher as can be seen in the comparison of the directional wave spectra of Figure
 7 4.1.2.
 (bottom).
 CaseLarge swells
 #2. Waves coming
 and Currentfrom the SW
 Almost are due
 Aligned to the formation
 Propagating of extra-tropical
 to the NE
 cyclones in the Gulf Stream region, which propagate north-easterly along the US Atlantic
 In the case when waves are almost aligned with the current (from the SW quadrant) and
 coast [38].
 the wind blows from the NE (see the red vector in the wave spectra) the spectral wave energy is
 Again, the simulation with currents is observed to produce broader wave spectra,
 higher as can be seen in the comparison of the directional wave spectra of Figure 7e,f. Large
 but since the waves are propagating in the same direction of the current the Hs decreases
 swells coming from the SW are due to the formation of extra-tropical cyclones in the Gulf
 almost 2 m (Hs = 10.02 m without currents and Hs = 8.20 m with current) (bottom panels).
 Stream region, which propagate north-easterly along the US Atlantic coast [38].

 (a) (b) (c)

 (d) (e) (f)
 Figure
 Figure7.7.The
 TheGulf
 GulfStream
 Streamsnapshot
 snapshot(a)
 (a) showing
 showing the
 the position of the
 position of the wave
 wave spectra
 spectra along
 alongthe
 thecurrent,
 current,current
 currentwith
 withvectors
 vectors(b),
 (b), wave field (c). Comparison of the 1D WAM wave spectra (d), the 2D WAM total wave spectrum (e) from the simulation
 wave field (c). Comparison of the 1D WAM wave spectra (d), the 2D WAM total wave spectrum (e) from the simulation
 without currents and considering the current (f) for the date 25 January 2019 at 00 UTC at location #43. Lat.: 37.167◦ N,
 71.417◦ W. Red arrow-wind direction, black arrow-mean wave propagation direction, blue arrow-current direction.

 Again, the simulation with currents is observed to produce broader wave spectra,
 but since the waves are propagating in the same direction of the current the Hs decreases
 almost 2 m (Hs = 10.02 m without currents and Hs = 8.20 m with current) (Figure 7e,f).

4.2. Analysis of the Characteristic Parameters Along a Transect Crossing the Gulf Stream
 This section focuses on the analysis of the Hs and mean wave direction obtained from
 simulations with and without currents along a transversal transect. The transect was cho-
J. Mar. Sci. Eng. 2021, 9, 42 11 of 15
 sen in such a way that it crosses the Gulf Stream along the 75°W meridian between the
 latitude 33°N and 36°N and the analysis is performed from the South to the North. The
 objective was to understand how the velocity gradient affects the Hs.
 4.2.ItAnalysis
 can be ofseen
 the Characteristic
 how the Hs Parameters Along the
 increases along a Transect Crossing
 transect the Gulfthe
 that crosses Stream
 Gulf Stream.
 The HsThis section focuses
 is correlated on current
 with the the analysis
 speedof(max
 the Hs1.75and mean
 m/s, wave
 see the direction
 right Y axis obtained
 red dashed
 fromand
 line), simulations with and
 its maximum without
 value currents
 (left panel along8,a blue
 Figure transversal transect.
 line with circlesThe transect
 (with was is
 current))
 chosen in such a way that it crosses the Gulf Stream along the 75 ◦ W meridian between
 observed in the centre of the Gulf Stream between the 34.5°N and 35°N. In addition, the
 the latitude ◦ N and 36◦ N and the analysis is performed from the South to the North.
 wind speed is33about 7.5 m/s, which does not favour the increase of waves.
 TheTheobjective was to understand
 Hs increases how thespeed
 with the current velocity
 onlygradient affects
 in the case thehas
 that Hs. currents, and it is
 It can be seen how the Hs increases along the transect that crosses the Gulf Stream.
 conditioned by the orientation of the waves with respect to the Gulf Stream (see directions
 The Hs is correlated with the current speed (max 1.75 m/s, see the right Y axis red dashed
 in the right panel), from latitude 34°N up to latitude 35.25°N. It is noteworthy that in this
 line), and its maximum value (Figure 8a, blue line with circles (with current)) is observed in
 case the current does no change appreciably◦ the wave◦propagation direction (Figure 8,
 the centre of the Gulf Stream between the 34.5 N and 35 N. In addition, the wind speed
 bottom
 is aboutpanel).
 7.5 m/s, which does not favour the increase of waves.

 (a) (b)

 (c)
 Figure 8. The
 Figure HsHs
 8. The and the
 and thecurrent
 currentspeed
 speed(a)
 (a)and
 andthe
 the mean
 mean wave propagationdirection
 wave propagation directionand
 andthe
 thecurrent
 current direction
 direction (b)(b) along
 along
 latitudes cross section from 33° ◦up to 36°N
 ◦ from the South to the North keeping the same longitude −75°
 ◦ West.
 latitudes cross section from 33 up to 36 N from the South to the North keeping the same longitude −75 West. Feather
 Feather
 plot showing the vectors (c).
 plot showing the vectors (c).

 InThe
 theHs
 case that waves
 increases witharetheopposed to the only
 current speed Gulf in
 Stream (seethat
 the case thehas
 green, the blue
 currents, andand
 it isthe
 dashed red lines,
 conditioned right
 by the panel of of
 orientation Figure 9), it was
 the waves withobserved
 respect tofrom the simulation
 the Gulf Stream (see with current
 directions
 the
 in same behavior
 the right panel),as in Figure
 from latitude8,34 ◦ Nthe
 i.e., up Hs increases
 to latitude ◦ N.line
 (blue
 35.25 It iswith circles)that
 noteworthy in the centre
 in this
 case the current does no change appreciably the wave propagation direction
 between the latitudes 34.5°N and 35°N of the Gulf Stream (left panel, Figure 9). Here the (Figure 8c).
 In the case that waves are opposed to the Gulf Stream (see the green, the blue and the
 dashed red lines, Figure 9a), it was observed from the simulation with current the same
 behavior as in Figure 8, i.e., the Hs increases (blue line with circles) in the centre between
 the latitudes 34.5◦ N and 35◦ N of the Gulf Stream ( Figure 9a). Here the wind speed is
 about 5 m/s blowing from the NW, so the Hs does grow noticeably (Hs = 1.48 m). On

J.J. Mar.
 Mar. Sci.
 Sci. Eng.
 Eng. 2020,
 2021, 8,
 9, x42FOR PEER REVIEW 13
 12 of
 of 16
 15

 wind speed is about 5 m/s blowing from the NW, so the Hs does grow noticeably (Hs =
 1.48 m). On the contrary the Hs (simulation without current, green line, left panel) does
 the contrary
 not show thisthe Hs (simulation
 increase of the Hs,without
 on thecurrent, green
 contrary, line, left panel)
 it decreases does not along
 with distance show this
 the
 increase of the Hs, on the contrary, it decreases with distance along the meridian
 meridian 75°W. However, the most noticeable effect is in the wave propagation direction 75◦ W.
 However,
 due to the the most(Figure
 current noticeable effect ispanel).
 9, bottom in the wave
 It canpropagation
 be observeddirection due to
 that without the current
 currents, the
 (Figure 9c). It can be observed that without currents, the direction
 direction changes from SW at 34°N to almost N at 35°N, while for the simulationchanges from 34◦
 SW atwith
 N to almost
 currents, theN at 35◦ N, while
 propagation for theissimulation
 direction with the
 constant along currents, the propagation direction is
 transect.
 constant along the transect.

 (a) (b)

 (c)
 Figure
 Figure 9.
 9. The
 The Hs,
 Hs, wind
 wind speed
 speed (U10)
 (U10) and
 and the
 the current
 current speed
 speed (a);
 (a); the
 the mean
 mean wind/wave
 wind/wavepropagation
 propagationdirection
 direction and
 and the
 the current
 current
 direction
 direction (b)
 (b) along
 along latitudes
 latitudes cross
 cross section
 section from
 from 3333°
 ◦ up to 36
 up to 36°N
 ◦ Nfrom
 fromthe
 the South
 South to
 to the
 the North
 North keeping
 keeping the
 the same
 same longitude
 longitude
 −75°
 −75◦West.
 West.Feather
 Featherplot
 plotshowing
 showingthe
 thevectors
 vectors(c).
 (c).

 As
 As shown,
 shown, in in general,
 general, the
 the Gulf
 Gulf Stream
 Stream speed
 speed varies
 varies from
 from the
 the high-speed
 high-speed centre
 centre ofof the
 the
 current
 current to
 to the
 the lower
 lower speed
 speed away
 away from
 from the
 the centre.
 centre. It It seems
 seems thatthat due
 due to
 to the non-uniform
 the non-uniform
 speed distributionacross
 speed distribution acrossthe the Gulf
 Gulf Stream
 Stream the the focusing
 focusing takestakes
 placesplaces generating
 generating steep
 steep waves,
 waves, when wind flows from the North (Figures 8 and 9), so the
 when wind flows from the North (Figures 8 and 9), so the wave energy is focused in the wave energy is focused
 in the centre
 centre of the of the stream.
 stream. With aWith a northerly
 northerly wind thewind the focusing
 focusing takeswhich
 takes place, place, concentrate
 which concen- the
 trate
 wavethe waveinenergy
 energy in the
 the centre of centre of thethat
 the stream stream
 maythatleadmay lead to dangerous
 to dangerous seas. seas.
 On
 On the
 the contrary
 contrary when
 when thethe wind
 wind flows
 flows from
 from South
 South thethe defocusing
 defocusing of of the
 the wave
 wave energy
 energy
 takes
 takes place
 place resulting
 resulting in in milder
 milder waves.
 waves.
 Some
 Some recommendations
 recommendations can can bebe made
 made regarding
 regarding the the navigation
 navigation in in the
 the region
 region of of the
 Gulf
 Gulf Stream.
 Stream. From
 From thethe hourly
 hourly mean
 mean maps
 maps of of the
 the Hs,
 Hs, Tp,Tp, and
 and the
 the surface
 surface current
 current itit can
 can be
 be
 seen that
 seen that dangerous
 dangerous places
 places for
 for the
 the navigation
 navigation are located
 located along the path of of the
 the Gulf
 Gulf Stream
 Stream
 showing high mean values of
 showing of Tp
 Tp (8–10
 (8–10s) that coincides
 seconds) with thewith
 that coincides current, as well as
 the current, asthe high
 well as
 Hs high
 the meanHs values
 meanranging from 3 tofrom
 values ranging 3.5 m.
 3 toThe
 3.5 most
 m. The dangerous area forarea
 most dangerous the navigation
 for the navi- is
 locatedisbetween
 gation the 36◦ Nthe
 located between and 38◦ N
 36°N and and
 38°Nbetween the 73◦ W
 and between theand73°W65◦and
 W (Figure 10a). This
 65°W (Figure 10,
 recommendation must be taken with caution since the performed simulations are short. In

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 16

 left panel). This recommendation must be taken with caution since the performed simu-
J. Mar. Sci. Eng. 2021, 9, 42 lations are short. In the future higher resolution simulations not only in time and 13space
 of 15
 but also in the wave spectrum are planned.
 The above results are in line with the reported ship accidents in severe weather in
 [39], where the region of the Gulf Stream was identified as one of the most frequent for
 the futuredue
 accidents higher resolution
 to higher wavesimulations
 heights for anot onlywave
 given in time and space but also in the wave
 period.
 spectrum are planned.

 (a) (b) (c)
 Figure
 Figure 10.
 10. The
 The averaged
 averaged maps
 maps over
 over the
 the simulation
 simulation winter
 winterperiod
 periodofof2019
 2019for
 for the
 the Hs
 Hs (a)
 (a) and
 and the
 the dangerous
 dangerous places
 places for
 for the
 the
 navigation (cyan dashed ellipse), the surface current (b) and the peak period map
 navigation (cyan dashed ellipse), the surface current (b) and the peak period map (c).(c).

 5. Conclusions
 The above results are in line with the reported ship accidents in severe weather in [39],
 where A the region of the Gulf
 characterization Stream was identified
 of inhomogeneities of theasocean
 one ofsurface
 the most frequent
 wave field for
 in accidents
 the Gulf
 due to higher
 Stream region wave heights
 has been for a given
 presented wherewave period.
 strong influence of current on waves take place.
 This was accomplished with numerical simulations using a third-generation wave model
 5. Conclusions
 with and without current.
 A general,
 In characterization of inhomogeneities
 it was observed that the Hs is of the ocean
 higher in the surface
 centre ofwave fieldStream
 the Gulf in the than
 Gulf
 Stream region has been presented where strong
 in the periphery. This fact has implications for the navigation. influence of current on waves take place.
 ThisWith
 was accomplished
 a northerly wind with numerical
 situation, simulations
 focusing using concentrating
 takes place, a third-generation waveenergy
 the wave model
 with
 in theand without
 centre of thecurrent.
 Gulf stream that may lead to dangerous seas. On the contrary when
 In general, it
 the wind flows from South was observedthe that the Hs is
 defocusing higher
 takes in the
 place centre of
 resulting in the Gulfwaves.
 milder Stream This
 than
 in the periphery. This fact has implications for the navigation.
 conclusion is important to be taken into account for the shipping industry.
 With
 The a northerly
 wave spectrum wind
 has an situation,
 elongatedfocusing
 shape takes place,
 and steep concentrating
 peak when wavethe andwave en-
 current
 ergy in the centre of the Gulf Stream that may lead to dangerous seas.
 are opposed. The effect of the Gulf Stream resulted in a resulted in a widening of the spec- On the contrary
 whenangular
 trum the wind flows from South the defocusing takes place resulting in milder waves.
 distribution.
 ThisTheconclusion
 limitationsimportant
 is to bestudy
 of the present taken lies
 intoon
 account for the
 three main shipping
 items: industry.
 the current field at 9 km
 The wave
 of spatial spectrum
 resolution does has
 not an elongated
 reproduce shape
 well and steep
 the eddies, thepeak when wave
 bathymetry dataandalsocurrent
 could
 are opposed. The effect of the Gulf Stream resulted in a resulted in a widening of the
 have a higher resolution than the used (Etopo1), and the spatial resolution of the wave
 spectrum angular distribution.
 model need to be increased as well to fully characterize the influence of the Gulf Stream
 The limitations of the present study lies on three main items: the current field at 9 km
 on the wave characteristics. In a follow-up study these three items will be considered.
 of spatial resolution does not reproduce well the eddies, the bathymetry data also could
 Author
 have aContributions:
 higher resolutionS.P.d.L:
 than Conceptualization;
 the used (Etopo1),methodology; validation;
 and the spatial formal analysis;
 resolution writ-
 of the wave
 ing—original;
 model need to C.G.S.: writing—review
 be increased as well to and editing.
 fully All authors
 characterize thehave read and
 influence agreed
 of the GulftoStream
 the pub-
 on
 lished version of the manuscript.
 the wave characteristics. In a follow-up study these three items will be considered.
 Funding: This work contributes to the Strategic Research Plan of the Centre for Marine Technology
 Author
 and OceanContributions: S.P.d.L.: Conceptualization;
 Engineering (CENTEC), which is financed bymethodology;
 the Portuguesevalidation;
 Foundationformal analysis;
 for Science and
 writing—original; C.G.S.: writing—review and editing. All authors have read and agreed
 Technology (Fundação para a Ciência e Tecnologia—FCT) under contract UIDB/UIDP/00134/2020. to the
 published version of the manuscript.
 Data Availability Statement: Data is available from the authors upon reasonable request.
 Funding: This work contributes to the Strategic Research Plan of the Centre for Marine Technology
 Conflicts
 and OceanofEngineering
 Interest: The authors declare
 (CENTEC), whichno conflict of
 is financed byinterest.
 the Portuguese Foundation for Science and
 Technology (Fundação para a Ciência e Tecnologia—FCT) under contract UIDB/UIDP/00134/2020.
References
 Data Availability Statement: Data is available from the authors upon reasonable request.
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 Conflicts of Interest: The authors declare no conflict of interest.
 doi:10.1029/TR029i002p00202.

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