Wave energy ﬂux variability in the Caribbean sea

Wave energy ﬂux (WEF) is assessed in the Caribbean Sea from a 60-year (1958–2017) wave hindcast. We use a novel approach, based on neural networks, to identify coherent regions of similar WEF and their association with diﬀerent climate patterns. This method allows for a better evaluation of the underlying dynamics behind seasonal and inter-annual WEF variability, including the eﬀect induced by the latitudinal migration of the Intertropical Convergence Zone (ITCZ), and the inﬂuence of El Ni˜no-Southern Oscillation events. Results show clear regional diﬀerences of the WEF variability likely due to both a clear regionalization of the WEF due to both the intensiﬁcation and migration of the ITCZ. WEF exhibits a strong semiseasonal signal in areas of the continental shelf, with maximums in January and June, in agreement with the sea surface temperature and sea level pressure variability. At larger scales, WEF shows a signiﬁcant correlation with the Oceanic Ni˜no Index depicting positive values in the central and western basin and negative ones at the eastern side.


Introduction
The wave energy flux (WEF) provides information on the magnitude and temporal variations of the energy transferred from the atmosphere to the ocean over selected periods of time (e.g.months, seasons or even years) [Dodet et al., 2010, Ardhuin andOrfila, 2018].It also extracts key details on sea surface waves that may not be detected from single parameters, such as significant wave height (Hs) or wave period (Tm-01), becoming a more suitable indicator to capture wave climate variations [Reguero et al., 2019].Long time series of WEF can be used to determine potential impacts on coastal zones, such as variations in the planform of beaches allowing to assess eventual impacts of future wave variations on coastal areas [Fiedler et al., 2015, Elshinnawy et al., 2017].Additionally, ocean waves is one of the renewable energy resources that has attracted more attention in the last years due to its potential capability of providing green and sustainable electricity offering several advantages with respect to other energy resources [Lin et al., 2019, Arinaga and Cheung, 2012, Liang et al., 2017].Therefore a precise characterization of the spatial and temporal variability of WEF is crucial to evaluate the local and regional impact of the evolving wave climate in the context of the ongoing global warming [Wiggins et al., 2019, Elshinnawy et al., 2017, Hanson et al., 2003].However, due to the scarcity of wave measurements around the world, to get the spatio temporal distribution of WEF we need to use validated wave hindcasts provided by numerical models [Mentaschi et al., 2017, Mirzaei et al., 2015, Waters et al., 2009, Iglesias et al., 2009].
Previous studies have analyzed inter-annual and long-term WEF variations associated with climate indices (e.g.El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Tropical North Atlantic index (TNA)) and climate change projections, respectively.On a global scale, [Reguero et al., 2019] found from a 60-year wave reanalysis that wave power has increased at a rate of 0.4% per year at global scale.These results indicate that the anthropogenic global warming is strengthening synoptic winds in some regions, thus favoring the generation of larger surface waves and affecting the global wave climate.[Reguero et al., 2015] characterized the mean wave power globally as well as its seasonal variability with a global wave reanalysis performed with WaveWatch3 model.Their results showed that the effect of the inter-annual variability is more prominent over the Northern Hemisphere, where the contribution of the seasonal variability is larger.[Wu et al., 2017] used ERA-Interim wave reanalysis data for the period 1997-2010 to evaluate WEF trends at global scale, as well as of time series of single parameters such as the significant wave height (H s ), mean wave period (T m−01 ), and wave direction (θ m ).Among the studied parameters, they found a significant increase in the magnitude of WEF, H s and T m−01 in southern mid-latitudes and in the western part of the North Atlantic and of the North Pacific.In contrast, they found a significant decrease of the same parameters in the eastern part of the tropical North Pacific [Wu et al., 2017].[Mentaschi et al., 2017] analyzed global trends of extreme WEF along global coastlines during the 21 st century under a high emission scenario (RCP 8.5).Results for this pessimistic projection would imply an increase of WEF up to 30% for most of the southern mid-latitudes, while in the Northern Hemisphere many coastal areas displayed negative trends.They also showed that significant long-term trends in the extreme WEF are related with the intensification of inter-annual signals such as ENSO and the North Atlantic Oscillation (NAO).On regional and local scales, several dedicated model-based studies have been developed to evaluate the wave energy resource, either the spatial distribution or the temporal variability [Liberti et al., 2013, Ponce de León et al., 2016, Liang et al., 2017, Canals Silander and García Moreno, 2019, Cuttler et al., 2020, Guillou et al., 2020], which has helped to improve the design and deployment of wave energy converters in the study areas.
Previous studies have already characterized the wave power in the Caribbean sea.[Ortega et al., 2013] identified the best sites for a wave farm near the small island of Isla Fuerte by means of numerical simulations.[Osorio et al., 2015], assessed the wave power potential in the Colombian Caribbean showing that the highest values of mean wave power are of 5-7 kW/m from December to April.This potential is relatively small compared to other places around the world, where powers of about 40 kW/m and above are considered profitable to implement wave farms.[Appendini et al., 2015] studied the wave energy potential in the whole Caribbean Sea from a 30-year wave reanalysis detecting that below the influence area of the Caribbean Low Level Jet (CLLJ), in the central Caribbean, the amount of wave power presents values between 8 -14 kW/m.They also mentioned the existence of large spatial wave power gradients, which need to be considered for the installation of energy extraction devices.[Guillou, 2020, Guillou et al., 2020] recently analyzed the wave energy and wave power resources for the whole North Atlantic, including the Caribbean Sea, using wave buoys at the open sea and a 30year reanalysis, respectively.Several metrics were compared to quantify the useful wave energy, as well as its seasonal variability.The maximum WEF was found during late fall (December and January) and late spring (June and July) with wave power ranges in the Caribbean Sea within the range of previous studies (5 -14 kW/m).Recently, [Orejarena-Rondón et al., 2022] used the same simulation we use in this work to analyze WEF trends in the Caribbean Sea, showing a decrease between 1958-2017 with an annual rate that oscillates between 0.01% and 0.2%, depending on the region.Here we go one step further to analyze the spatial and temporal variability of WEF in the Caribbean Sea from 1958 to 2017 using a novel approach with which coherent regions that show similar WEF are distinguished according to their associated wind pattern.By applying this method we get new insights on the physical processes that drive seasonal and inter-annual WEF changes, including the impact of ITCZ migration and ENSO events.
The article is structured as follows: the main Caribbean Sea features are described in section 2. Data set and methods are outlined in section 3. Section 4 shows the main results including model validation, regional characterization of WEF and surface wind, as well as their temporal variability at seasonal and interannual scales.Finally, in section 5 we discuss the main results in the context of the current literature and the main conclusions are summarized.

Study area
The Caribbean Sea is located between latitudes 8.1 • N -13.6 • N and longitudes 84.52 • W-59.7 • W, being bordered by the Lesser Antilles at the east, the Greater Antilles at the north, the eastern portion of Central America at the west and the northern coasts of South America at the south (Figure 1).Wave dynamics is mainly controlled by the westward surface trade winds, which show a large seasonality, and a low-level wind core with higher speeds that gives origin to the Caribbean Low Level Jet (CLLJ).The CLLJ has its kernel at a height of around 925 hPa, although can reach heights over 800 hPa and is located in the center of the basin [Amador, 1998, Poveda and Mesa, 1999, Poveda et al., 2006, Chunzai, 2007, Orfila et al., 2021].Wind seasonality is associated to the meridional migration of the ITCZ, which is also responsible for the path and penetration of transient features as cold fronts and tropical storms [Poveda et al., 2006, Poveda, 2004, Andrade and Barton, 2013].The meridional oscillation of the ITCZ responds to the seasonal insolation cycle.During the austral summer the ITCZ is located between Colombia and Ecuador, whereas it shifts northward in the boreal summer.When the ITCZ is located between 0-5 • S, the northern trade winds dominate in these regions with an average speed that varies between 8 and 15 m/s [Andrade, 1993].This seasonality is modulated by regional sea surface temperature and sea level gradients which add a semi-seasonal component [Chunzai, 2007].
Regarding atmospheric instability conditions, there is little rainfall from December to April over the Colombian basin and in the west of the Antilles.Conversely, in the Caribbean coasts surrounding the Gulf of Darien (which includes coasts of Colombia, Panamá and Costa Rica), it rains throughout almost the whole year [Andrade et al., 2013].By contrast, when the ITCZ is located at a latitude between 10-12 • N, from August to November, the weaker southern trade winds (with a mean speed ∼4 m/s) reach the Colombian basin, contributing to the formation and even strengthening of tropical convective storms that may reach hurricane category over the western Caribbean Sea [Andrade et al., 2013].As a result, the precipitation caused by the displacement of the ITCZ only affects the Colombian basin below 10 • N. Consequently, trade winds (and hence the CLLJ) permanently remain above La Guajira peninsula.The rest of the year there is a transition period between the aforementioned seasons, in which trade winds weaken and some rainfall comes over the Colombia basin from April to June), while from June to August trade winds strengthen and rainfall decreases.The latter transition time is locally known as "Veranillo de San Juan" from its name in Spanish [Poveda et al., 2006, Andrade et al., 2013].
Winds and rainfall are sensitive to the arrival of oscillations such as easterly waves, with periods of 7 days, and cold fronts, coming from North America and crossing the Caribbean towards the East in about 10 to 14 days generating precipitation and rising wind stress on its way [Andrade et al., 2013, Alvarez-León et al., 1995].Large-scale signals such as the Madden-Julian Oscillation have longer periods (40 to 50 days) and have been detected in sea surface temperature and in rainfall records in Santa Marta, Colombia, at a latitude above 11 and Molares, 2003, Andrade et al., 2013].Moreover, there is also a strong interannual variability associated with ENSO that affects both Atlantic and Caribbean coastal areas.[Huang et al., 2002, Enfield andMayer, 1997] determined that at the end of the year, when El Niño events tend to become stronger, trade winds weaken over the eastern Caribbean Sea at a latitude between 10 • N and 20 • N, extending until Africa.In contrast, in the western part of the Caribbean Sea trade winds strengthen during El Niño events.3 Data and Methods

Wind data
Surface wind fields used to force the The Simulating WAves Nearshore (SWAN) model in the study area correspond to the JRA-55 simulation performed by the Japan Meteorological Agency.This data was the first complete reanalysis in covering the last half century , and the first one that applied a four dimensional variational analysis [Kobayashi et al., 2015].This set of global atmospheric data is suitable to study multidecadal variability and the relation of wave climate with climate change [Japan Meteorological Agency, 2013].Output fields provide the 10 m height wind speed (u w , v w ) on a mesh of 23 × 43 grid points with a spatial resolution of 0.5625 • × 0.5616 • .The data cover the whole study area from 84.3746 • W, 7.5819 • N (lower left corner) to 60.1871 • W, 19.9371 • N (upper right corner) from 1958-2017 (both included) with a 3-hourly temporal resolution.

SWAN Model
The SWAN model solves the wave action balance equation for the propagation of the wave spectrum, which allows for realistic estimations of wave parameters in the open ocean and in coastal areas [Booij et al., 1999].The SWAN domain covers an area of 2600 km × 1175 km distributed into 229 × 101 grid cells (Figure 1).The bathymetry of the Caribbean Sea was obtained from Colombian Hydrographic Service nautical charts as well as from the general ocean bathymetric chart GEBCO.
Waves were simulated in non-stationary mode using the JRA-55 wind fields.Windinduced wave growth was configured as exponential following the formulation of [Komen et al., 1984], while nonlinear deep water interactions were parameterized following the Webb-Resio-Tracy method.Other relevant processes, such as wave breaking, whitecapping energy dissipation, and bottom friction were included in the simulations.The integration time step was set as 30 minutes and H s , T m−01 , and θ m output data were recorded every 3 hours in each domain grid cell.H s and T m−01 were validated through a comparison with in situ wave data measured by the NOAA-42058 buoy, which is located in the central Caribbean Sea (Figure2).The wave reanalysis we use in this work is published at [Orejarena-Rondón et al., 2021a].

Wave Energy Flux (WEF) calculation
Departing from the 3-hourly SWAN model output fields (H s , T m−01 , θ m ), the monthly mean WEF was determined for the period 1958 -2017.The WEF was computed as: where ρ is the seawater density in kg/m 3 , g is the gravity acceleration, T m−01 is the mean period, H s is the significant wave height and − → k is the wavenumber vector.Departing from these components, we carried out a spatial and temporal characterization of the mean WEF in the Caribbean basin through a Self-Organizing Map analysis.Similarly, we have analyzed the inter-annual variability of the monthly mean WEF over time through a correlation analysis with ENSO indices.

Self-Organizing Map (SOM)
Self-Organizing Map is a statistical tool used to compress the information contained in a large amount of data into a single set of maps [Kohonen, 1982, Teuvo, 1997], reducing the high dimensional feature space of input data to a lower dimensional network of units called neurons.This unsupervised learning neural network is able to extract patterns from large data set mimicking the topological distribution of the neurons response in the brain.Learning processes are carried out by an interactive presentation of the input data to a preselected neuronal network, which is modified during the iterative process.Each unit is represented by a weight vector with a number of components equal to the dimension of the input data.During each iteration, the neuron whose weight vector is closest to the presented sample input data vector, called Best-Maching Unit (BMU), is updated together with its topological neighbors toward the input sample (see [Hernández-Carrasco and Orfila, 2018] for a more detailed description of the SOM process).When the probability density function of input data is approximated by SOM, and each unit is associated with that reference pattern that has a number of components equal to the number of variables in the data set, the training process finishes.Thus, this process can be interpreted as a generalization of similar observations.In this study, a joint SOM analysis is applied over the monthly mean fields of both WEF and surface wind in the area covered by the 60-year wave reanalysis.In the case of the spatial analysis, since each iteration has associated a time and a location of the sample, we can obtain the evolution of a particular pattern computing the BMU for each sample.In the temporal domain the analysis of the neurons provide temporal patterns and the BMU is used to localize in space the temporal variability, providing regions of similar co-variability patterns.

Correlation and Cross Wavelet Transform Analysis
To explore the link between monthly mean WEF and ENSO at inter-annual scales we have proceeded as follows.First, we performed a direct correlation analysis between the Oceanic Niño Index (ONI) and the monthly mean WEF time series at every grid cell within the study area (Figure 12).Second, the cross wavelet transform (XWT) and wavelet coherence (WTC) analysis is applied between the ONI index and the time series associated to each of the 9 regions determined by SOM.The XWT between the temporal signals of the mean WEF and ONI reveal those regions where energy variance is more correlated giving also information about their phase relationship.The XWT of any two time series x n and y n is defined as W XY (s) = W X (s)W Y * (s), where * denotes the complex conjugate.Furthermore, the cross wavelet power is defined as |W XY (s)| and the complex argument as arg(W XY (s)).The latter represents the relative local phase between x n and y n , which we will depict by arrows.The WTC spectrum highlights how large is the covariance of these signals, regardless of the high power display [Grinsted et al., 2004, Nalley et al., 2016, Restrepo et al., 2019].The degree of coherence of XWT is given by the following coefficient: where S is a smoothing operator with values ranging between 0 (no correlation) and 1 (perfect correlation).The relationship between WEF and ONI is identified by the phase angle observed in the spectrum.An in phase relationship is indicated by the arrows pointing to the right.On the other hand, an out of phase relationship is indicated by arrows pointing to the left.Arrows that do not point straight to the right or to the left indicate a lagged correlation relationship.

Wave model validation
Validation of SWAN simulation is performed with the NOAA buoy 42058, which is located in the central Caribbean Sea, using both H s and T m−01 (see Figure 1).Conversely, due to the unavailability of other parameters, only modeled H s can be validated with those buoys located near of San Andres Island: buoy SAI Dimar and NOAA buoy 42059, which are located at the west and east of the basin, respectively (see Figure 1).In the case of the buoy NOAA-42058, a good fit between in-situ and model data was obtained.For H s , bias, correlation and Willmot coefficients values of 0.064, 0.83, and 0.9 were obtained respectively, while for T m−01 , bias, correlation, and Willmot coefficients have values of 0.089, 0.74 and 0.77, respectively (Figure 2).For the other two buoys, a good fit was found between modeled H s and in-situ H s estimates.Correlation coefficients for buoy NOAA 42059 and buoy SAI Dimar were 0.7 and 0.91, respectively (Figure 3).Willmot coefficient values were 0.822 and 0.974 for buoy NOAA 42059 and buoy SAI Dimar, respectively, while bias coefficients for buoy NOAA 42059 and buoy SAI Dimar of 0.03 and 0.0034, respectively.

Spatial patterns of monthly mean WEF over the Caribbean Sea from SOM Analysis
As mentioned above, spatial patterns are obtained by applying a joint SOM analysis between the monthly mean WEF and the monthly mean horizontal wind fields.and P7), are associated with the meridional migration of the ITCZ throughout the year (Figure 7).P1, with an occurrence of 22.6%, is associated with the dry season (December to April, see Figure 7), with the highest probability occurring from January to March (> 35%).P7, with an occurrence of 14.6%, is associated with the transition season.This pattern is presented with a low frequency of occurrence during May and August, and with high frequency during June and July (> 35%), when the "Veranillo de San Juan" occurs.P6, with an occurrence of 10.4%, is associated with the wet season (from August to November).The highest frequency of occurrence of this pattern is presented during the months of September and October (> 35%).This pattern also appears in May, a month that corresponds to the transition period, but with lower frequency of occurrence (15%).
Although with less probability of occurrence, other patterns (P2, P3, P4, P5, P8 and P9) also take place in any of the three climatic seasons.For instance, P2 and P4, with 6.7% and 4.4% probability of occurrence, have a low probability of occurrence during the dry season (March, April, May and December).P5 and P8, with 2.6% and 7.9% probability of occurrence each one, are associated with the transition season.P9, with 10.4% probability of occurrence, is associated with the wet season (low frequency of occurrence during June and October and intermediate probability during May, August and September).P3, with 13.3% probability of occurrence, is presented randomly throughout the year (see Figure 7): the highest probability is presented in November (30%), the intermediate one in April and December (20%), and low one in February and March (10%).
In order to assess the spatial and temporal changes of both WEF and surface wind fields we have computed the standard deviation of every SOM pattern (Figure 5 for the WEF and Figure 6 for the wind).The patterns with the largest variability are P1, P6 and P9 for WEF and P1 and P9 for wind, being in all cases restricted to the western Caribbean basin.As observed, the increase in the magnitude of the WEF and wind speed, are the result of both the displacement of the ITCZ and the intensification of trade winds.

Temporal patterns of WEF over the Caribbean Sea from SOM analysis
To better explore the dominant direction of WEF, we have applied a temporal SOM analysis over zonal (F x ) and meridional (F y ) components monthly mean WEF.As we use 3 × 3 neurons again, this analysis also provides 9 zones of covariability in the Caribbean Sea (Figure 8). Figure 9 shows time series of F x and F y components for every region in top and bottom panels, respectively.The sign (+/-) in the abscissas indicates the direction of each components: a negative value indicates a direction towards the west in the zonal component and towards the south in the meridional component, whereas a positive value indicates a direction towards the east in the zonal component and towards the north in the meridional one.Most of time series conserve the same sign, which allows to clearly identify the dominant direction.
As seen, the zonal component is generally two times larger than the meridional one.According to the magnitude of WEF we can distinguish three groups of zones: the largest values (in absolute magnitude) are observed in zones 7, 4, 1 (in decreasing order), located in the center and western areas of the Caribbean Basin, from 70 • W, extending toward the south and to the west of the basin (Figure8).Time series of WEF associated with zone 7 (Tp7 in top and bottom panels) reach values between -1300 and -400 (W/m) for F x , and between -220 and 0 (W/m) for F y (Figure9), which indicates that WEF is predominantly oriented WSW-W over the 60 years.Similar results are found in zone 4, but with a stronger meridional component.In contrast, zone 1 shows weaker components and slightly turned to the south (oriented SW-WSW).
Moderate values of WEF are observed in zones 8, 5 and 2. These regions cover the center Caribbean basin between 64 • W and 70 • W, and extend toward the zone 7 (Figure 8).In zone 8, time series of u and v components take values between -1000 and -350 (W/m), and between -60 and 100 (W/m), respectively (Figure9).It indicates that WEF is predominantly oriented toward the W. Similarly, components in zone 5 are also mainly oriented toward the W, with values between -850 and -300 (W/m) and between -100 and 40 (W/m) (Figure9).Components of zone 2 show weaker zonal values, between -700 and -250 (W/m), and a stronger merid-Fig.7 Seasonal occurrence probability of each spatial pattern of mean WEF and wind horizontal fields shown in Figure 5 and Figure 6.
ional component, between -240 and -40 (W/m), which is reflected in a slightly turned to the South dominant orientation (WSW).
Finally, the lowest values of WEF are observed in zones 9, 6 and 3, which are located at latitudes above the zone 8, in the East of the basin, and off the coastal zones of Colombia, Venezuela and Nicaragua (Figure 8).Time series of F x and F y in zone 9 show values between -650 and -250 (W/m) and between 20 and 140 (W/m), respectively (Figure 9).The latter depicts a predominant WNW-W orientation.Similarly, time series of zone 6, with values between -500 and -200 (W/m) and between -40 and 60 (W/m) for u and v, respectively (Figure9), show a dominant W-WNW orientation.As occurred in zones 5 and 4, components are also slightly turned southward in zone 3, with values between -400 and -150 (W/m) and between -80 and 0 (W/m) for u and v, respectively (Figure9), with a predominant W-WSW orientation.

Analysis of WEF direction at seasonal scale
Departing from time series of Figure 9 we study the direction of mean WEF at a seasonal scale for the 9 zones depicted in Figure 8.To obtain the annual cycle we compute the 60-year monthly mean for each zone and component (Figure 10).
Results illustrate a semi-seasonal signal in the zonal component of all regions characterized by two peaks.These peaks take place in January and June (see the most negative values), while the minimum values (in magnitude) are reached in April and September.These relative extremes are associated to the latitudinal migration of the ITCZ, which affects the magnitude of trade winds.Regarding the  meridional component we find a mixed behavior: Zones 1, 2 and 4 also show two peaks (see Figure 10, bottom panel), while in northern regions such as 6, 8 and 9 there is only one peak, which takes place in May.
Figure 11 summarizes previous results showing the resultant 60-year monthly mean direction of WEF for every pattern shown in Fig. 8.As seen, the largest WEF (¿1000 W/m) comes from east and east-northeast and correspond to patterns P7 and P4.Other modes such as P2, P3 and P9 represent weaker configurations (100-500 W/m), although waves keep coming from east-northeast or east-southeast, thus depicting small fluctuations in the direction throughout the year.This small variation in the direction is expected from dominant trade winds.The direction of the WEF ranges between the SW (P1, P2, P4 and P7) and NW (P8 and P9).The largest WEF is found in the areas corresponding to P1, P4 and P7.

Relationship between ENSO and the inter-annual variability of WEF
To evaluate the influence of ENSO on the inter-annual variability of WEF we have performed a correlation analysis between both variables.To this end, we use monthly time series of ONI and monthly mean WEF spanning from 1958 to 2017 (both included).Results show relatively large simultaneous correlations (of Next, we have computed the wavelet coherence (WTC) for all zones provided by the temporal SOM decomposition.Results shown that ENSO is correlated and coherent with the mean WEF over a long range of time scales and frequencies (Figure 13).The spectrum reveals a strong co-variability between ENSO and WEF in all regions for periods ranging from 24 to 32 months, and from 32 to 64 months.The longest period with significant correlations is 74 months (≥ 6 years).The relative phase indicates that ENSO leads WEF by 45 • at periods between 32 and 64 months, and by 90 • for periods between 64 and 72 months in all regions (see arrows in Figure 13 pointing downward).For example, for periods between 32 and 64 months WTC revealed a lag (ENSO leads) during 1993 and 1999 in all zones (see the large coherence during El Niño 1998).Moreover, there is a longer lag (ENSO leads) during 2001 and 2011 for regions 4-9.The WTC also reveals significant coherences between ENSO and mean WEF at a period between 24 and 40 months, as well as an increase in the coherence at a period between 24 and 92 months at the end of the two series, mainly in regions 1, 4 and 7 (Figure 13A-C, respectively).The coherence between 24 and 40 months is initially in-phase for years 1964and 1967, lagged (ENSO leads) between 1972and 1974, and almost in-phase between years 1978and 1983. .Regarding the periods between 24 and 92 months, the coherence is lagged (ENSO leads) from 1993 to 2017.The larger positive correlation between WEF and ONI during El Niño events (either during Canonical or Modoki events, although is larger during Modoki) is likely caused by the strengthening of the CLLJ, especially in the Colombian basin [Wang, 2007, García-Martínez andBollasina, 2020].

Discussion
Departing from a 60-year wave simulation we have analyzed the spatial and temporal variability of the mean wave energy flux (WEF).First, we have validated the simulated significant wave height (H s ) and mean wave period (T m−01 ), against in-situ data from buoy 42058 of NOAA (Figure 2).Correlation, Weibull and Bias coefficients shown a good agreement between modeled and observed data.The database here used contributes to reduce the lack of available information on wave parameters in the Caribbean Sea [Orejarena-Rondón et al., 2021a].Indeed this simulation is the longest in comparison to other wave reanalysis available in the Caribbean Sea [Arias et al., 2009, Dagua et al., 2013, Appendini et al., 2015, Osorio et al., 2016], and has been employed for marine energy analysis [Orejarena-Rondón et al., 2022], but can also we used for studies of coastal vulnerability, to analyze climate variability, or to study open sea extreme wave conditions for coastal and offshore engineering, among other.Data is freely accessible in the repository https://nimbus.imedea.uib-csic.es/s/JEaPEeeQNLPFJ3S[Orejarena-Rondón et al., 2021b].
By applying a spatial SOM analysis over monthly mean WEF data we have regionalized WEF variability in the Caribbean Sea.Thus, wave information was classified into 9 patterns that collect the complex behavior of WEF (magnitude  1993, Andrade and Barton, 2013, Poveda et al., 2006].The patterns (P i ) with more probability of occurrence are: P1 with 22.64% (dry season), the P6 with 17.36% (wet season) and the P7 with 14.58% (transition season), all of them associated with the growth in wave height and the change in wave period of waves as they move westward, reaching its maximum for P1 off the Colombian coasts.Other patterns are less frequent and distribute throughout the seasons: P4 and P2 occur during the dry season; P3 during the wet season (November); P5 and P8 occur in the transition season and at the beginning of the wet season.Finally, P9 occurs during both transition and wet seasons.
SOM analysis was also applied to surface winds used to force the model.Results are consistent with the 9 patterns obtained in the analysis of WEF (Figures 5 and 6 top panel).In this case, we observed the influence of the Caribbean Low Level Jet more toward the east between longitudes 68 • W -78 • W and latitudes 11 • N -18 • N, which differ from the influence zone of WEF (72 • W -83 • W, and 10 • N -16 • N).A plausible explanation is the large fetch in the Caribbean Sea, which allows wind waves some space to growth until they reach their most energetic state (Figures 5 and 6, top panels).
After that, we performed a temporal SOM analysis over the zonal and meridional component of WEF in the Caribbean Sea.As a result, we identified 9 zones of co-variability where WEF has different magnitudes and directions (Figures 7  and 8).Overall the zonal component is more energetic, due to the dominant trade winds.In particular, the most energetic zones are 7, 4, 1 and 8 (Figure 9 in the top panel).Regarding the meridional component, the most energetic zones are the 1, 4, 7 and 2. These results illustrate why the resultant direction is sometimes to the west (P1).
On the other hand, departing from above time series of WEF we have computed the seasonal cycle by calculating the 60-year monthly mean of zonal and meridional components, respectively.As a result, we get the seasonal cycle for each component and every region.Figure 10 illustrates the influence of ITCZ latitudinal displacements.Interestingly, the zonal component depicts a seasonal cycle with two peaks in all regions.However, the meridional component has one peak in the three regions located more to the north in the Caribbean Sea.The more energetic is the region the more clearly defined are the two peaks since the Caribbean Low-Level Jet, whose semi-annual cycle has been reported in previous works [Chunzai, 2007, Orfila et al., 2021], has a stronger influence.Unsurprisingly, the two peaks are more visible in the meridional component in those zones below 12 • N (zones 1, 4 and 2).This is consistent with the description by [Andrade, 1993, Andrade and Barton, 2013, Poveda et al., 2006], who described that northernmost position of ITCZ is located between 10 • N -12 • N. Above of this latitude the direction of WEF differs, as shown in Figure 11 for zones 6, 8 and 9.
Next, we have explored the relationship between ENSO and WEF at interannual scales.A correlation analysis show a strong positive correlation in the central part of the basin (0.4), lower but still positive in the Gulf of Darien (0.1-0.2), and negative off Venezuela (-0.3 to -0.1, Figure 12).This behavior is consistent with the findings of [Enfield andMayer, 1997, Huang et al., 2002], who determined that when the Pacific warm anomalies during an ENSO event reach their maximum at the end of the year, trade winds weaken over the eastern Caribbean Sea at a latitude between 10 • N and 20 • N, and extend until Africa, while in the western Caribbean Sea trade winds strengthen.
Finally, to determine the periods and lag times of common variability between ENSO and WEF we compute the Wavelet Coherence (WTC).Results suggest the existence of a statistical between changes in ONI and WEF in different time periods, thus indicating that the monthly mean WEF is sensitive to changes in ENSO.All regions were correlated with the ONI for periods between 24 and 40 months during years 1964-1967, 1972-1974 and 1978-1983, characterized by the occurrence of large warm events in the eastern Pacific.This correlation occurs with the same phase in all periods, being larger between zones 4-9 (see Figure 13).Similarly, a strong correlation during years 1993-2017 is observed in all regions for a period that spans from 24 to 92 months, especially in zones 1, 4 and 7.
CIENCIAS (Call 727) and POGO-SCORE Visiting fellowship at the Mediterranean Institute for Advanced Studies.Aurthors acknwoledge DIMAR (Dirección General Maritima from Colombia) for the wave parameters supplied for the model validation.J.M. Sayol thanks the joint funding received from the Generalitat Valenciana and the European Social Fund under grant APOSTD/2020/254.

Fig. 1
Fig. 1 SWAN domain used for the 60-year wave simulation in the Caribbean basin.Red triangles indicate the location of buoys used for the validation: Buoy SAI DIMAR, NOAA buoy 42058, and NOAA buoy 42059, ordered from west to east.

Fig. 2
Fig. 2 Validation of: (A) significant wave height,Hs, and (B) wave period (T m−01 ) in the central Caribbean Sea between SWAN simulation and observations provided by buoy 42058 (Figure 1).Color scale of dispersion diagrams corresponds to associated density of data used for validation.The linear regression is represented by a black dashed line.

Fig. 3
Fig. 3 Validation of Hs in the west and east of Caribbean basin (see buoys SAI DIMAR and NOAA 42059 in Figure 1, respectively).Color scale of dispersion diagrams corresponds to associated data density used in the validation.The linear regression is depicted by a black dashed line.

Fig. 5
Fig. 5 Spatial patterns of mean wave energy flux (WEF) given by a 3 × 3 SOM analysis with their direction in the Caribbean basin (top panel).Standard deviation for the above mentioned spatial patterns (bottom panel).The percentage in each pattern reflects its total occurrence probability in %.

Fig. 6
Fig. 6 Spatial patterns of wind fields obtained from the SOM analysis given by a 3 × 3 with their respective direction, in the Caribbean basin (top panel).Standard deviation for the computed above mentioned spatial patterns (bottom panel).The number at the bottom-right in each pattern corresponds with total occurrence probability in %.

Fig. 8
Fig. 8 Regions given by the temporal SOM analysis.SOM was applied with 3 × 3 neurons over the monthly mean WEF.We refer to these patterns in Figure and Figure 10.

Fig. 9
Fig. 9 Temporal patterns provided by a 3 × 3 SOM time domain analysis computed over the monthly mean WEF for zonal (Fx) and meridional (Fy) components (top and bottom panels, respectively).Names on the top-left side of every panel: Tp1, Tp2, ..., Tp9 refer to patterns shown in Figure 8. µ and σ are the mean and the standard deviation of every time series, respectively.Unit in W/m.

Figure 11
Figure11summarizes previous results showing the WEF roses at each region.The direction of the WEF ranges between the SW (P1, P2, P4 and P7) and NW (P8 and P9).The largest WEF is found in the areas corresponding to P1, P4 and P7.

Fig. 11
Fig. 11 Monthly mean WEF roses for the amplitudes shown in Figure 9, which correspond to the 9 zones displayed in Figure 8. Units in W/m.

Fig. 12
Fig. 12 Map of spatial correlation between monthly mean WEF and ONI for the study area.White color indicates a non statistically significant correlation.Red (blue) color indicate a positive (negative) correlation.