Long-term spectral wave climate in the Black Sea based on directional  wave spectra

Long-term spectral wave climate in the Black Sea based on directional wave spectra | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Long-term spectral wave climate in the Black Sea based on directional wave spectra Khalid Amarouche, Adem Akpınar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2596229/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Directional wave spectra describe complex sea states in frequency and directional domains and provide more detailed information than the bulk wave parameters. Spectral wave informations are important for the design of ships and offshore structures. Using hourly directional wave spectra hindcasted for a period of 42 years between 1979 and 2020, long-term spectral wave climate in the Black and Azov Seas was assessed. To determine the climatic wave spectrum, variance densities are averaged over the frequencies and directions for annual and seasonal, monthy scales. Futhermore, The individual wave system observed in each directional wave spectra are determined referring to the independent spectral peak at each observation. The different sea states conditions, including the uni-modal and multi-modal wave systems are classified and analysed; The energy, frequency, and direction of the three first prominent individual wave system peaks are deeply evaluated as a function of the sea state conditions. Occurrences as foction of spectral peak density and directions of the prominent individual wave system peaks are also computed and discussed. The results reveal that multi-modal spectra are more frequent in most regions, although the highest peak density values and lowest peak frequencies were observed within the wave spectra of uni-modal sea states. The spectral peak densities, frequencies, and directions depend both on the number of wave systems in the wave spectrum and on the geographic location. The first peaks in the wave spectra are mostly derived from two dominant directions and ~ 54% of the peaks had a density greater than 2 m2/Hz. In contrast, the second and third peaks in the wave spectra are typically derived from three or more dominant directions and rarely exceed a density of 2 m2/Hz. Directional wave spectra Spectral wave climate spectral partition wind-wave multi-peak wave spectra individual wave systems. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction A thorough statistical understanding of the ocean wave environment is crucial for many scientific and engineering applications (Portilla-Yandún et al. 2015 ). Sea conditions are a combined result of reactions from multiple wave systems, and the synthesis of these multiple wave systems produces the sea surface states. Only part of the resulting surface waves is aligned with the wind direction due to complex energy transfers from the atmosphere to the sea (Teixeira and Guedes Soares 2009 ). Wave climate analysis can be performed more efficiently by using wave spectra since the spectra provide more detailed information than the bulk wave parameters (Shimura and Mori 2019 ), such as significant wave height (H m0 ) and mean wave period (T m02 ). The wave spectrum describes complex sea states in frequency and directional domains and provides a comprehensive representation of the existing wind-sea and swell wave combinations (Boukhanovsky and Guedes Soares 2009 ). Spectral partitioning of wave data can provide the scientific community with more detailed and comprehensive information (Albuquerque et al. 2021 ). For an accurate sea simulation, the directional wave spectrum constitutes the basis for investigating the interaction between waves and marine structures (Goda 2018 ). Additionally, for the design of ships and offshore structures, methods for assessing wave-induced stresses do not only require estimates of bulk wave parameters but also data on the directional spectrum of waves (Boukhanovsky et al. 2007 ). For instance, Considering changes in the bulk wave parameters fails to properly incorporate the existence of positive and negative variations in the wave climate within the directional spectrum (Lobeto et al. 2021 ). The bulk parameters provide a good account of the wave characteristics in cases of uni-modal seas, but they fail to adequately represent the sea state in more complex situations (Lucas et al. 2011 ; Portilla-Yandún et al. 2015 ). Marine structures are subjected to all types of sea states that can occur during their lifetime, and it has been demonstrated that in many situations, the sea states are a result of the combination of more than one wave system, and in this case, the frequency spectrum exhibits two peaks (Teixeira and Guedes Soares 2009 ), or more. The wave climate data are mainly treated as the long-term statistics of significant wave heights H m0 , mean periods T m02 and mean directions θ at the global ocean (Challenor et al. 2007 ; Liang et al. 2019 ; Smith et al. 2021 ; Colosi et al. 2021 ) or regional scale (Kamranzad 2018; Vieira et al. 2020 ; Young et al. 2020 ; Sreelakshmi and Bhaskaran 2020 ; Amarouche et al. 2021a ). However, in recent decades, the interest in wave climate studies based on directional wave spectrum has been raised (Portilla et al. 2009 ; Hamilton 2010 ; Lucas et al. 2011 ; Portilla-Yandún et al. 2015 ; Vledder and Akpinar 2016 ; Jiang and Mu 2019 ; Jiang 2020 ); noting that directional spectra provide information that cannot be obtained from the commonly used method based on integrated wave parameters (Lobeto et al. 2021 ). According to (Toffoli et al. 2005 ), There are indications that wave trains traveling along different directions in general and crossing seas, in particular, should be seen as possibly dangerous conditions. The shipping and offshore industry are accounting for the situation of the combined sea in the design approach (Boukhanovsky et al. 2007 ). The present study, therefore, aims to perform a long-term (42 years) spectral wave climate analysis for the Black and Azov seas. The long-term climatic wave spectra are evaluated by averaging the climatic distribution of spectral wave density as a function of frequency and direction on annual and seasonal scales. On the other hand, a spectral partitioning of individual waves was performed, and the long-term occurrence of mono-peak wave spectra (uni-modal seas), double-peak (bimodal), and multi peaks (multi-modal) wave spectra. The spectral partitioning was performed using an innovative approach presented by (Portilla et al. 2009 ; Portilla-Yandún et al. 2015 ) and initially applied in the Black Sea by (Vledder and Akpinar 2016 ). The approach consists of pre-processing the wave spectra using smoothing tools to follow the steepest ascending variance density path until a peak is reached and finally to merge all points climbing to the same local peak (Portilla et al. 2009 ). However, in the present study, the individual wave partition is studied based on the peak characteristics of all analyzed directional wave spectra. The corresponding frequency, direction, and energy of each peak are obtained from the no smoothed wave spectra. A relatively similar approach was adopted in previous studies (Hamilton 2010 ; Lucas et al. 2011 ). Hamilton, ( 2010 ) applied statistical sampling and clustering algorithms to classify the wave spectral shape observed in shallow water locations off northwest Australia and claimed that the classification and identification of distinct wave systems made it possible to describe wave spectral data sets more accurately without losing information. Thus, Lucas et al., ( 2011 ) performed a classification of the wave spectra in North-eastern Atlantic and Portuguese coastal waters based on wave spectral shape. They proposed five classes of spectral wave systems based on the number of peaks and spectral shape characteristics. Bukhanovsky et al., ( 2013 ) used the same approach proposed by (Lucas et al., 2011 ) in several locations around the world, including one location in the southern part of the Black sea and one in the Azov Sea. The spectral wave data used to perform the present study was developed using a SWAN (Simulating WAve Nearshore) model (Booij et al. 1999 ; Ris et al. 1999 ). The model was spatially calibrated for the Black Sea and the Sea of Azov based on satellite altimeter and buoy measurements (Amarouche et al. 2021b ), and validated against 14750 spectral measurements collected at the Utrish coast during a period of ~ 11 months (Amarouche et al. 2023 ) because the model's accuracy in estimating the wave spectrum and an awareness of the model output uncertainty is critical for a reliable assessment of the spectral wave climate. 2. Material And Methods Considering the importance of the spectral wave climate in offshore and coastal activities, we strongly support the statement of Boukhanovsky et al., ( 2007 ) that it is now crucial to promote the development of more complete wave data atlases that incorporate spectral wave climate descriptions. The present study consists of a detailed assessment of long-term spectral wave climate in the Black and Azov Seas. For this purpose, hourly directional wave spectra for a period of 42 years between 1979 and 2020 were analyzed. Two widely used approaches are considered for processing the directional wave spectra. The first approach consists of averaging wave variance densities over the frequency and direction for annual and seasonal scales by considering the whole data set. According to Lucas et al., ( 2011 ), the computed results based on this first approach allow us to determine the climatic wave spectrum, initially termed by Buckley ( 1988 ). This simple approach in analyzing the long-term climatic wave spectra was used in several previous studies, e.g. (Panigrahi and Swain 2010 ; Corbella and Stretch 2014 ; Espindola and Araújo 2017 ; Patra et al. 2019 ). The second used approach consists of a detailed assessment of the different wave systems occurring in the Back Sea and the Sea of Azov, including the uni-modal and multi-modal wave systems. This approach consists in partitioning the individual wave system observed in each directional wave spectra to determine the number of wave systems by referring to the independent spectral peak at each observation, followed by a classification of the observed sea states during the analyzed period, to determine the occurrence of uni-modal and diferentes multi-modal wave systems. Furthermore, the peak energy, peak frequency, and peak direction of the first three spectral wave partitions are deeply evaluated. The analyses are performed on 25 selected locations shown in Fig. 1 . Table 1 provides further information about the depth at each location and their distance to the coastal line. The methodology used to process the different wave systems based on the shapes of the directional wave spectra by clustering the mono and multi-peak wave system was recently used by several researchers to study the spectral wave climate at different locations around the world, e.g. (Hamilton 2010 ; Lucas et al. 2011 ; Bukhanovsky et al. 2013 ; Portilla-Yandún et al. 2015 ). Table 1 The geographic charachteristics of 25 selected reference locations Station nbr Lon Lat Depth (m) Distance from the coastal line ( ˚) Selected locations S1 36 46 -12.0 0.501 S2 37.5 46 -10.3 0.347 S3 31 45.5 -41 0.779 S4 30 44.5 -65 0.521 S5 32 44.5 -1265 0.980 S6 36 44.5 -1157 0.514 S7 37.5 44.5 -14 0.000 S8 29 43.5 -79 0.393 S9 31 43.5 -1356 1.924 S10 33 43.5 -2156 1.110 S11 35 43.5 -2205 1.234 S12 37 43.5 -2111 1.288 S13 39 43.5 -2038 0.520 S14 28 42.5 -49 0.224 S15 30 42.5 -2164 1.308 S16 32 42.5 -2204 0.830 S17 34 42.5 -2050 0.518 S18 36 42.5 -1946 0.766 S19 38 42.5 -2146 1.400 S20 40 42.5 -1839 0.731 S21 29 41.5 -111 0.241 S22 31 41.5 -1279 0.423 S23 37 41.5 -199 0.201 S24 39 41.5 -1976 0.451 S25 41 41.5 -1501 0.266 To summarise, the whole study was performed in four main steps, i. calibration of the model and evaluation of its accuracy in estimating wave spectra (Amarouche et al., 2021b ). ii. development of a long-term wave hindcast derived from the calibrated and validated model. iii, partitioning of the wave spectrum performed based on two-dimensional wave spectra. iv. long-term statistical analysis of wave spectral data considering each wave system in 25 sites in the Black Sea and the Sea of Azov. In the following section, we provide more detailed information on the used model, the used data accuracy, and the spectral partitioning and processing method. 2.1. Development of the spectral wave database At present, the only way to obtain a piece of long-term information on directional spectral wave climate is through the use of spectral wind-wave models. The buoy and radar-measured wave spectra can only serve for a limited period and at limited sea locations. To perform this study, a long-term database of a 42 years’ period was developed using a calibrated model SWAN with a time resolution of 1h. The SWAN model was calibrated at a spatial scale based on satellite observation to ensure a balanced accuracy over the whole basin. The spatial calibration allows an accurate evaluation of the spatial variability in the wave climate, even in the location in gaps of buoy measurements. The SWAN model calibration reduces the underestimations of wave energy observed by considering the default model setting in the Black Sea as documented in previous studies (Moeini and Etemad-Shahidi 2007 ; Kamranzad et al. 2013; Rascle and Ardhuin 2013 ; Akpınar et al. 2016 ; Akpinar and Ponce de León 2016 ; Atan et al. 2017 ; Kutupoğlu et al. 2018 ; Bingölbali et al. 2019 ). The model is calibrated after a sensitivity test to the used wind and whitecapping source terms and to the used wind forces. Thus, the tuneable coefficient (C ds ) which is related to the wave dissipation by whitecapping, was tuned to obtain an optimal value. The calibrated SWAN model was run in non-stationary mode with a simulation time-step set to 30 min. The wind and whitecapping source term of Komen et al. , (1984) was chosen based on the calibration results. The C ds coefficient value is set at 0.8 − 5 . The JONSWAP (Hasselmann et al. 1973 ) shape of the spectra in both frequency and direction is used with a gamma ray peak enhancement parameter of 3.3. The directional wave energy density spectrum is discretized with a constant increment of 35 bins for the frequencies ranging between 0.04 Hz and 0.625 Hz and 36 bins for the spectral wave directions. The ERA5 reanalysis wind (Hersbach et al. 2020 ) was used to force the model for the whole simulated period. ERA5 data were developed by the European Centre for Medium-Range Weather Forecasts (ECMWF) and provided by the Copernicus Climate Change Service (C3S) Climate Data Store https://cds.climate.copernicus.eu/ (last accessed in 15.06.2021). The ERA5 wind data are characterized by a spatial resolution of 0.25° × 0.25° and cover the period from 1979 to the present. The ERA5 wind is considered the most accurate wind forcing for wave modelling in the Black sea based on the results obtained in previous studies (Van Vledder and Akpinar 2015 ; Çalışır et al. 2021 ; Amarouche et al. 2021b ; Soran et al. 2022 ), which used and compared different wind reanalysis. Thus the accuracy of the ERA5 wind reanalysis was shown in several other studies at different seas (Baordo et al. 2020 ; Sharmar and Markina 2020 ; Beyramzadeh et al. 2021 ; Amarouche and Akpınar 2021 ). Concerning the computation grid, an unstructured mesh grid was used. This grid is developed using OceanMesh2D 1.0 (Roberts et al. 2019 ). The spatial resolution is 300m in the nearshore and increasing gradually to 11km in the offshore. This grid covers all the Black Sea and Azov Sea and the model output are obtained for all grid points for a period of 42 years and a time resolution of 1 hour. The developed data base contains both directional and non-directional spectral data, managed in yearly NetCDF folders. 2.2. Spectral data accuracy and uncertainty The evaluation of spectral wave model precision in the estimation of directional wave spectrum is rarely documented. In general, wave models are evaluated based on wave parameters such as H m0 and T m0 and the mean direction, but the accuracy of the spectral energy distribution as a function of frequency and direction is usually not considered. The accuracy of the model in estimating H m0 may reflect a good accuracy in the total energy spectrum of the bi-modal waves, but it can never indicate accuracy in the spectrum as a function of the frequency, direction, and energy of the peaks, nor accuracy in the multi-modal energy spectrum. The wave model used for developing the directional wave spectra hindcast data is evaluated by (Amarouche et al. 2023 ) based on 14,710 spectral measurements collected over about 11 months on the Utrish coast using a Datawell DWRG-4. Uncertainties related to the spectral wave model are discussed in (Amarouche et al. 2023 ) in terms of the annual and seasonal averaging and also in estimating the individual spectrum shapes. The average wave spectra estimated by the SWAN model show a good accuracy compared to the measurements, with a slight overestimation of ~ 10% in spectral energy between 0.13 and 0.17 Hz. In terms of spectral direction, a maximum bias of 20 degrees is observed. It should be noted that the measurement buoy is located very close to the coast at a depth of 42m within a complex bathymetric zone. In terms of the model's accuracy in estimating individual spectrum shapes, the statistical errors showed a correlation greater than 0.7 for the frequency range from 0.08 Hz to 0.5Hz and exceeding 0.8 in a range of high spectral frequency (0.15–0.32 Hz) in the Utrish buoy. In addition, it should be noted that the frequency-based RMSE results are more pronounced between 0.1Hz and 0.17Hz, with a maximum RMSE of 0.09 m 2 /Hz. 2.3. Spectral wave partition and processing approach The long-term spectral wave climate assessment is a complex process due to the significant quantity of information contained in one spectral measurement. Directional wave spectra may provide information on real sea states. It provides information on the individual wave systems and allows us to define the different wind-sea, and swell partitions. The partitions contained in each spectrum can be characterized by a peak direction, a peak frequency, and a peak energy. By determining the different partitions of the estimated wave spectra, statistical analysis of the wave spectral systems over a long period may provide deep information on the spectral wave climate in the Black and Azov Seas. Thus, by averaging the spectral variance density as a function of time, frequency, and direction, we can determine a climatic wave spectrum as defined by (Buckley 1988 ). Several operational methods are proposed for spectral wave partitioning. Some methods can permit the separation of the wind sea from the swell partition, and others allow the determination of more than two partitions in the case of multi-modal wave systems. The most straightforward proposed approach to spare the wind sea from the swell is to set a partition frequency value to separate the low-frequency waves (swell) and the high-frequency waves (wind sea). Among the empirical approach used to define the partition frequency value f par , we can note the Earle (1984) approach. The latter is based on the frequency spectrum of Pierson and Moskowitz forced by the local wind speed and can be approximated as follow (Earle 1984): $${f}_{par}=0.8\times {f}_{PM}$$ 1 $${f}_{PM}=0.13\times \frac{g}{{U}_{10}}$$ 2 where f PM denotes the peak frequency of the Pierson and Moskowitz spectrum in a fully developed wind wave (Pierson and Moskowitz 1964 ), g is the gravity acceleration, and U 10 is the wind speed at 10m above the sea surface. The partition frequency can also be determined without wind information by considering the wave steepness proposed by (Wang and Hwang 2001 ). In these approaches, the wind sea and swell are distinguished by a separation frequency value derived from the peak frequency of the steepness function based on the Pierson–Moskowitz spectrum (Wang and Hwang, 2001 ). Those partitioning methods are operational. However, they only allow us to separate the wind sea from the swell and do not allow us to determine all wave partitions in case of a multi-modal wave system or multi-peak spectrum. To divide all probable wave partitions, Gerling ( 1992 ), proposed a 2d partition scheme using the directional wave spectra. He proposed an algorithm allowing wave spectral partition in terms of frequency and direction. Following the same approach proposed by Gerling ( 1992 ), (Hasselmann et al. 1996 ) and (Hanson and Phillips 2001 ) developed and used another improved algorithm. (Hasselmann et al. 1996 ) applied the approach for the partition of two-dimensional wave spectra obtained from the synthetic aperture radar (SAR) image spectra, and (Hanson and Phillips 2001 ) proposed another algorithm as an automatic Wave Identification and Tracking System (WITS). The partition scheme of (Hanson and Phillips 2001 ) consists in isolating the peaks in the spectral direction and to combine the wind-sea peaks based on the wave age criterion. The wave age criterion is defined as And in the deep water $${f}_{p}\ge \frac{g}{2\pi }{\left[{C}_{wind}\times {U}_{10} \times \text{cos}\left({\theta }_{W}- {\theta }_{WS}\right)\right]}^{-1}$$ 4 In which c p is the wind sea's phase speed at a particular peak frequency, C wind is a tuneable factor in guaranteeing all potential wind sea peaks are considered. θ w and θ ws refer to wind direction and wind-sea direction successively. As a result, the first partition is formed by combining the partitions whose peak fits these requirements and classifying them as wind seas. In the case of multi peaks spectra, (Hanson and Phillips 2001 ) algorithm first determines the swell peaks and then combines the adjacent swell peaks as mutual swell belonging to the same swell system. These methods permit the identification of all different partitions as a function of their frequency and direction in the multi-peak wave spectra. Referring to the idea initiated by Gerling, ( 1992 ), Portilla et al., ( 2009 ) proposed an improved operational approach in which the wave spectra are pre-possessed using a smoothing tool as noise-removal in a two-dimensional scale. By the next, based on the smoothed wave spectra, the steepest ascending variance density paths are followed until the peak, and all points connected to the same peak are grouped as an individual wave partition. Based on the same idea, the peak locations of each individual wave system are located. Noting that the presented study focuses on the spectral wave climate in the whole Black and Azov Seas, and not in one location, the number of information is significantly high for 42 years. The present study is mainly focused on the occurrence of the different waves system, and the peak characteristics of each individual partition are statistically analysed in terms of their frequency, direction, and energy. The plot in Fig. 2 shows an example of the results obtained by partitioning directional wave spectra and identifying the peaks at each partition and their characteristics. The different combined sea states are classified based on the number of the wave system in 5 classes, considering the wave spectra with one wave system (mono peak) and those of 2 to 5 wave systems (multi-peak). The partition order of each wave spectra is determined based on their peak energy from the most energetic (partition 1) to the least energetic. The total number of the directional wave spectra is 368,196 for a period of 42 years and a time resolution of 1h, for a total of 23 offshore locations over the Black Sea and 2 stations in the Sea of Azov are considered for the evaluation of the spatial variability in the spectral wave climate. 3. Results And Discussion 3.1. Long-term average wave spectra The analysis of two-dimensional spectral data provides a better understanding and better characterization of the wave climate behavior in the Black Sea and the Sea of Azov. The hourly 2D wave variance densities (wave spectra) (in frequency and direction domain) were averaged and visualized on annual, seasonal and monthly basis at 25 selected offshore stations (see Fig. 1 ), representing different regions of the Black Sea and Sea of Azov. The results are showed in Figs. 3 – 5 . Two-dimensional intensity spectra are used to identify the main wave peaks according to their direction and frequency. The lower averaged values of the spectral variance density with an energy above 0.01m 2 /Hz are neglected and not ploted to better observe changes focusing on the most occuring and most energetic wave systems. The mean variance density calculated for a period of 42 years (Fig. 3 ) shows that only the southwestern Black Sea (location A21) and southeastern Black Sea (location A25) regions are characterized by a single main averaged density peak of (> 0.2m 2 /Hz), while in the rest of the Black Sea the wave spectrum shows an occurrence of multiple averaged density peaks ranging from two to three peaks (> 0.2m 2 /Hz). The directional spectrum of the waves in the eastern part of the Black Sea shows the occurrence of two opposite and energitic (> 0.05m 2 /Hz) spectral density peaks (S13, S19, S20, S23, and S24). The peaks formed by the waves traveling eastward in this region have higher frequencies. This reflects the presence of wind waves from northeast to southeast. In the center of the Black Sea (locations S10, S11, S17) the spectral density plots show multiple peaks density (> 0.2m 2 /Hz) from different directions and frequencies. The Northeast and Northwest peaks are located at high frequencies, while the Southwest and Southeast peaks are located at lower frequencies. Moreover, no southern spectral density with an average value above 0.01m 2 /Hz was observed in the center of the Black Sea. In the northwestern part of the Black Sea (locations S3 - S5 and S9) spectral peaks are multiple. The Northern and Northeastern and eastern wave peaks have high intensity and low frequencies, while the West to Southwest wave peaks have lower intensity and higher frequencies. In the Northeast Black Sea (locations S6 and S7), the wave spectrum shows the presence of two main peaks, the more intense peak is from West to Southwest and the second peak is from East to Southeast. In the eastern Sea of Azov (location S2), the spectrum shows the presence of three main peaks with a frequency of about 0.2 Hz from the North-Northeast-Southeast and South-Southwest directions. In the western Sea of Azov (location A1), two opposed peaks with low intensity and low frequency of 2.5 Hz are observed in the East-Northeast and West-Southwest directions. Those peaks reflects a dominance in wind sea at this region. In terms of wave intensity, the Western and Southwestern part of the Black Sea is characterized by the highest spectral intensity from Northeastern and Eastern origin, where the mean intensity variance reaches 0.4 m 2 /Hz. Thus, the wave intensity observed in the center is concentrated in the directions from Northeast and Northwest to West. On a seasonal scale (Fig. 4 ), there is clearly a seasonal variability in the spectral density distribution as a function of wave direction and in terms of the main peak number and variance density values. During the winter period, a wave peak distribution similar to the values observed in Fig. 3 for the annual average is observed in term of direction. However, the averaged densities peaks are located in a lower frequency and mainly around 0.1Hz, reflecting the intensity of the swell during the winter. Another exception appears for the station located southwest of the Black Sea near the Bosphorus (location S21), where a southwest peak at a low frequency of ~ 0.25 Hz and a variance density of ~ 0.04m 2 /Hz appear. This peak reflects the exceptional wind-sea activity in that location (S21) during the winter. The averaged variance density reached 0.7 m 2 /Hz for the multiple peaks observed in the western part of the Black Sea (locations S4, S5, S8-S10, S15, and S16) in the winter. Moreover, this maximum intensity is observed in the spectrum of double main peaks in the center (locations S10, S11, and S17), while in the eastern region the spectral intensity is lower and the peaks are generally more pronounced from the Southwest, West and Northeast directions (locations S13, S19, S20, S23, S24, and S25). In the Sea of Azov (locations S1 and S2), the eastern region is more energetic, with the presence of three to four main peaks in different directions; Southwest, Southeast, EastNortheast and NorthNortheast. On the other hand, the western part of the Sea of Azov has lower intensity and three peaks from the Southwest, West and Northeast directions. During the spring, the wave spectrum shows a lower density of high frequency waves. Moreover, the seasonal average variance density is very close to the annual average variance density presented in Fig. 3 . Moreover, in the spring, the Northeast and East variance intensity values in the eastern part of the Sea of Azov (location S1) and northeast of the Black Sea (locations S6 and S7) are more consistent with the annual average. In summer, the wave spectrum shapes mostly show a single peak in the eastern and western Black Sea and two peaks in the center, except in the eastern Sea of Azov (location S2), where three peaks with low intensity are observed. The southern coast of the Black Sea is exposed to more energy during the summer months compared to the northern coast. During the autumn, in the western and eastern parts of the Black Sea, the wave spectra are very similar to those observed in spring and to the annual average. In the northeastern part of the Black Sea (locations S6 and S7) and in the eastern part of the Sea of Azov (location S1), the variance of the mean intensity from the Northeast direction is greater in autumn than in spring. On a monthly scale (Figs. 5 a to 5 c), the average spectral wave regime shows that four different wave patterns occur throughout the year. It is noteworthy that the months of November, December, January, February and March present a spectral pattern with the same number of peaks and a very similar range of variance intensity in the Black Sea, while in the Sea of Azov there is no similarity. April, May and June show a similar spectral wave pattern with lower variance intensity. July and August are the two calmest months. During these two months, wave spectral patterns are generally single-peaked along the southern coast (locations S21 - S25) and eastern part (locations S13, S19, and S20) and double-peaked in the rest of the Black Sea and the Sea of Azov. September and October shows the same spectral regime in the northern part of the Black Sea, while in the eastern part, the shape of the wave spectrum during October is different. In October, low-frequency waves can be observed moving from the East to the Southeast. These results show a different classification of the seasons in terms of wave spectral regime. The results for winter are similar to those for November, December, January, February, and March. The results obtained for the spring are more similar to April, May, and June, while the results for summer are more reflective of July and August. Finally, the results for the autumn are more comparable to September and October, except for the eastern part of the Black Sea. 3.2. Occurrences of unimodal and multi-modal sea states The individual wave system partitions at each directional wave spectra are identified and characterized based on peak density, frequency, and direction. The number of individual wave systems along the hourly time series are computed for each wave spectra. The obtained results allowed as to determine the occurrences in percent of the unimodal and multi-modal sea states around the Black Sea and the Sea of Azov (Fig. 6 ). The results show a low occurrence of unimodal sea states at most regions of the Black Sea (the locations S3-S13, S15-S20, S22, and S24). The occurrences of the unimodal sea states varied between 7% and 19%. However, in the Sea of Azov, the occurrences in unimodal sea states are more important, with 48% in the west and 51% in the east. Four other locations in the Black Sea (the locations S14, S21, S23, and S25) are also dominated by unimodal sea state and located on the south-eastern and the south-western coasts of the Black Sea. The unimodal occurrences at those locations varied between 36% and 40%. The bi-modal sea state shows a high occurrence at all locations at both the Black Sea and the Sea of Azov, with a minimum occurrence of 23% in the eastern part of the Azov Sea and the western part of the Crimean Peninsula and a maximum of 36% off the central coast of Turkey. The tri-modal sea states are highly occurring in the most of Black sea (the locations S14, S21, S23, and S25). With 24–32% of the total sea states, except in the Black Sea's south-western and south-eastern coasts, the maximum occurrence of the tri-modal wave system is 17%. Thus, the occurrence of a tri-modal wave system in the Azov Sea is lower and varies between 12% in the east and 14% in the west. The occurrence distributions of the quad-modal and quint-modal sea states follow the distribution of the tri-modal sea state with lower abundance. The quad-modal and quint-modal sea states are more occurring in the Black Sea's offshore locations (S5, S9 - S12, and S16). In the Sea of Azov, the sea states with more than three individual wave systems are less than 8%. 3.3. Characteristics of spectral wave systems The characteristics of individual wave systems partitions at all wave spectra are defined considering their number and the peak density, frequency, and direction of each individual wave system. Based on the number of wave systems in the directional wave spectra, the sea conditions are defined as unimodal or multi-modal. It was noticed that the multi-modal sea states are more dominant in the Black Sea (Fig. 6 ). However, the information on occurrence of the individual sea states should be completed by the character of each wave system at different sea state conditions. The occurrences of multi-modal sea states in a specific location do not necessarily reflect a higher energy distribution. For instance, the results presented in Fig. 7 show that the averaged densities of the prominent peaks (1st peaks) are more critical during the unimodal sea state events in the Azov Sea (the locations S1 and S2) and at most of the Black sea (the locations S3-S8, S10, S12-S15, S18-S21, S24-S25). In those locations, the average densities of the prominent peaks of all wave spectra containing one individual wave system are more important compared to the average density of the main peaks in a wave spectrum containing two or more wave systems. However, an exception is observed at four locations (S9, S11, S17, and S22) where the averaged densities of the first main peak are more important in the case of bi-modal sea states and even with tri-modal sea states at location S22. With the increase in the number of individual wave systems, the average density of the primary peak generally decreases. We can conclude that the maximum peak energy in the Azov Sea and a large part of the Black Sea can be more interesting to study during the unimodal wave sea states. The information on the spectral peak density is important for evaluating the fatigue life of marine structures (Zeinoddini et al. 2015 ). The highest average in peak density exceeding 2 m 2 /Hz is observed in the Black Sea's south-western basin. Concerning the average density of the 2nd main peak, we can also notice a dependence on the sea state conditions and the number of individual wave systems. The averaged density of the 2nd main peak is more critical at the locations S1 - S3, S7, S8, S14, S15, S21, and S24 but is more important during the tri-modal wave system at the remaining locations. The average density at the 2nd peak is less important during the quad-modal and quint-modal sea states. The highest density of the 2nd main peaks in the 2d wave spectrum is observed in the western Black Sea basin. The average density of the 2nd peak in the Azov Sea does not reach 0.2m 2 /Hz. The 3rd main peak averaged density in the wave spectrum is neglected at the Sea of Azov and significantly low in the Black Sea. The average density of the 3rd peak is more important during the quad-modal and quint-modal sea states except at the locations S7 and S21, where the averaged density is more important for the tri-modal sea states. Looking at the results of the peak frequency average (Fig. 8 ) computed for the prominent three peaks and during different sea state conditions, we noticed that the frequency of the 1st peak is lower compared to the 2nd peak frequency, which is slightly lower compared to the 3rd peak frequency. Thus, we can notice a dependence of the peak frequency on the number of individual wave systems. At most locations, the 1st, 2 nd, and 3rd peak frequency averages increase by increasing the number of individual wave systems. However, an exception for the 1st peak frequency averages is observed at the locations S13, S20, and S22. In locations S13 and S20, the frequency of the 1st peak during the bi-modal sea states is lowered. In the location S22, the frequency of the 1st peak during the unimodal sea state is higher than all 1st peak frequency averages in multi-modal sea states. The same finding is observed at the locations S13, S20, and S24, comparing the averaged frequency of the 2nd peak and 3rd peak during the bi-modal and tri-modal sea states successively to their frequency in the presence of more individual wave systems. Based on those results, we found that the highest peak energy and the lowest frequency occur during the unimodal sea states in the most of the Black Sea. High peak density at low frequency can reflect a concentred amount of energy which can be dangerous for marine structures. Regarding results of averaged peak direction of the main three peaks (Fig. 9 ) computed for the different sea state systems, we can notice a clear dependence of the spectral peak means direction to the number of wave systems. The mean directions of the 1st main peak during the unimodal sea states are largely different from the mean directions of the 1st main peak during the multi-modal sea states. The differences can exceed 30ͦ at most locations depending on the number of wave systems. The same situation is observed for the 2 nd, and the 3rd peaks' mean directions. The mean peak direction changes remarkably depending on the number of wave systems. These results reflect that different climate patterns govern the various individual wave systems. Evaluating the possible connection of the individual wave system to the distinct climate patterns anomaly may provide a better understanding of wave climate in the Black Sea. At the location S5, we can observe the highest difference of > 75ͦ between the 1st peak mean direction computed during the unimodal sea states and the 1st peak mean direction computed during the multi-modal sea states systems. Considerable differences are also observed between the 2nd and 3rd peak directions at different sea systems. It is important to notice that the averaged direction will depend more on each wave system's most occurring direction. Thus, the averaged direction does not necessarily provide accurate information about the individual wave system direction if the dominated waves originated from two or more dominated directions. Thereby, in the following section, we are presenting the occurrences of the first three peaks in the directional wave spectra as a function of directions, densities, and frequencies. 3.4. Occurrences of individual wave system Based on individual wave systems; characterized by their peak variance density and peak direction, the occurrences of the first main peaks are estimated as a function of directions. The results are presented using wave roses for 25 locations in the Black and Azov Seas (Fig. 10 ). The results show a considerable difference in the directional distribution of the 1st, 2nd, and 3rd peaks. The variation in peak direction is less important for the first wave system peak of the wave spectrums. The 1st peak mainly originated from two dominant directions in offshore locations or one dominant direction in the locations close to the coastal line. However, the 2nd and 3rd peaks of the wave spectra can be originated from a wider direction range. Three to four dominant directions of the 2nd and 3rd peaks can appear in the offshore locations. The main differences we can notice regarding the distribution of individual spectral peaks as a function of direction can be observed in the western part of the Black Sea (the locations S12, S13, S19, S20, and S25), where the 2nd peaks in the wave spectra are highly occurring from a western sector contrarily to the 1st peaks which are rarely occurring from the Eastern origin. In the western location S1 of the Azov Sea and the Odessa shelf (the location S3), the directions of the 1st peaks from the North sector are rare. However, the occurrence of the 2nd peaks originating from the North are more considerable. On the south-western coast of the Black sea (the location S22), we noticed a high occurrence of wave spectra with the 2nd peak of south-west origin, while similar directions for the 1st peaks in the wave spectra are rare in the same location. Concerning the distribution in spectral peak densities as a function of wave directions, we can notice that peak density exceeds 2m 2 /Hz from mostly all occurring directions and at all locations. The 1st peaks of > 0.5m 2 /Hz constitute ~ 50% of the total occurring waves at most locations. The variance density exceeding 5m 2 /Hz is also observed in all Black Sea regions and the eastern location of the Azov Sea, however, with a low rate and mainly from the most dominated directions. For the 2nd peaks, the variance densities are lower, while the 2nd peaks in wave spectra with a variance density > 0.5m 2 /Hz are considerably occurring at mostly all locations except at S1, S3, and S25. The 2nd peak with a spectral density > 2m 2 /Hz also occurred in the western and central basins of the Back Sea and in the eastern location of the Azov Sea. Regarding the density of the 3rd peak in the spectrum, the peak densities rarely exceed 0.5m 2 /Hz. Thus, mostly the spectral densities of the 3rd peaks in the wave spectra are 2 m 2 /Hz are S5 and S9. 4. Summary And Conclusions This study performed a long-term assessment of spectral wave climate based on hindcasted two-dimensional wave spectrum data in the Black and Azov Seas. The directional wave spectra are evaluated by averaging the climatic distribution of spectral wave density for each frequency and directional range. The annual, seasonal, and monthly wave spectral averages are computed and mapped for 25 grid locations. The individual wave systems was identified for each directional wave spectra. The unimodal and multi-modal sea states are filtered and occurrence of each sea states systems was defined. Considering the individual wave systems’ peak caracteristics, long term averaged density, frequency and directions of the three first prominent individual wave system peaks are computed as a function of the sea state conditions. Finally, occurrences of the peak directions of the main individual wave systems at all directional wave spectra was computed as function of the spectral peak density. The obtained results, allow to describe with further details the wave climate of the Black and Azov Seas. The longterm averages of the variance densities in directional wave spectra at annual, seasonal and monthly scales allow us to define the locations of density peaks as a function of direction and frequency. Most locations in the Black Sea and Azov Sea are characterised by two or more critical peaks from different directions and frequency. According to this evidence, the long-term study of wave climate based only on bulk parameter H s and mean period and mean directions is not sufficient to describe the wave climate regime in the Black and Azov Seas. For instance, if the wave density spectrum is consentrated at two or more directional ranges, the computed mean wave directions of the mixed sea my provide a wrong information. The occurrences of unimodal and multi-modal sea states showed that multi-modal spectra are more occurring, however, referring to the average density and frequency of the main wave system peak during the unimodal sea states, we noticed a highest peak density values and lower peak frequency at most location comparing to the main peak density values observed for multi-modal sea states. An exception was noticed at (S9, S11, S17, and S22), where the highest value in the averaged densities and the lower peak frequency in the 1st peaks are more observed during the bi-modal sea states. The spectral peaks’ densities, frequencies and directions are depending on both the number of wave systems in the wave spectra and to the geographical location. We concluded that a multi-modal sea state in a specific location do not necessarily reflect a higher energy in the total wave spectra, and that unimodal sea states may contain more concentrated energy with low frequency in several locations (e.g. S8, S14, S15, and S22). The occurrences of peaks density of the individual wave systems as a function of directions presented using the individual wave system peak density roses allowed us to conclude that the 1st peaks in the wave spectra are mainly originated from two dominant directions and that ~ 54% of the peaks’ densities exceed 2 m 2 /Hz. However, the 2nd and 3rd peak in wave spectra are occurring from 3 or more dominant directions and the rarely exceeding the 2 m 2 /Hz. Declarations Acknowledgments The work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 119N480. The authors acknowledge the European Center for Medium-Range Weather Forecasts (ECMWF) for providing ERA5 wind data through the Copernicus Climate Change Service (C3S) Climate Date Store. We also acknowledge the General Bathymetric Chart of the Oceans (GEBCO, www.gebco.net) for providing the bathymetry data. Funding The work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 119N480. Competing Interests The authors have no relevant financial or non-financial interests to disclose. Author Contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Khalid Amarouche. The first version of the manuscript was written by Khalid Amarouche and edited by Adem Akpinar. All authors read and approved the final manuscript. Data Availability The datasets generated during and/or analyzed during the current study are not publicly available at this stage, but are available from the authors on reasonable request. References Akpinar A, Ponce de León S (2016) An assessment of the wind re-analyses in the modelling of an extreme sea state in the Black Sea. Dyn Atmos Ocean 73:61–75. https://doi.org/10.1016/J.DYNATMOCE.2015.12.002 Akpınar A, Bingölbali B, Van Vledder GP (2016) Wind and wave characteristics in the Black Sea based on the {SWAN} wave model forced with the {CFSR} winds. Ocean Eng 126:276–298. https://doi.org/10.1016/j.oceaneng.2016.09.026 Albuquerque J, Antolínez JAA, Gorman RM et al (2021) Seas and swells throughout New Zealand: A new partitioned hindcast. 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J Geophys Res Ocean 101:16615–16629. https://doi.org/10.1029/96JC00798 Hersbach H, Bell B, Berrisford P et al (2020) The ERA5 global reanalysis. Q J R Meteorol Soc 146:1999–2049. https://doi.org/10.1002/QJ.3803 Jiang H (2020) Wave Climate Patterns from Spatial Tracking of Global Long-Term Ocean Wave Spectra. J Clim 33:3381–3393. https://doi.org/10.1175/JCLI-D-19-0729.1 Jiang H, Mu L (2019) Wave Climate from Spectra and Its Connections with Local and Remote Wind Climate. J Phys Oceanogr 49:543–559. https://doi.org/10.1175/JPO-D-18-0149.1 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2596229","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":177080176,"identity":"5e2c8ac4-7d73-428d-a247-84a590ff779c","order_by":0,"name":"Khalid Amarouche","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABKklEQVRIiWNgGAWjYBACCQkGxgMJbFAeYwODHAM7UBTMO4BTCwOKFmMGZoQWIB+HFgYkLYkNhLRIzm5+cOBBmV00/+zDxyR+7rBJ33CYx/DGj18Mcnw3EtgfV2BqkZY5ZnAg4Vxy7oxzaWmSvWfScoFajC17+xiMJW8kMDaewdQiJ5FgcCCxjTm34QyPmTRj22GQFjMJ3h6GxA0gLVhcJieR/gGopT53PkTL/3QDoBbJvz0M9bi0SEvkgGwBGg7RciABpEWa5wdDggEOLZIzcgqAfjmeu/EMW7Jlb1uy4czDbMXWsg0ShjPPPGyciUWLxI30jQ9/lFXnzjvDfPDGzzY7eb7jzRtvvvljA2QkH/iILZSxA8Y2UNRgjRac4A8pikfBKBgFo2CYAwByH3Ms/zHaTwAAAABJRU5ErkJggg==","orcid":"","institution":"Bursa Uludağ University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Khalid","middleName":"","lastName":"Amarouche","suffix":""},{"id":177080177,"identity":"71ac959e-13c9-4ed0-84a9-0aa7291b71e1","order_by":1,"name":"Adem Akpınar","email":"","orcid":"","institution":"Bursa Uludağ University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Adem","middleName":"","lastName":"Akpınar","suffix":""}],"badges":[],"createdAt":"2023-02-16 19:29:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2596229/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2596229/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":33231170,"identity":"897d920b-167f-436b-9c8d-9288ccf19b94","added_by":"auto","created_at":"2023-02-21 14:33:06","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2053425,"visible":true,"origin":"","legend":"\u003cp\u003eDirectional wave spectrum with three individual wave systems and three spectral peaks (P1,P2 and P3) located at different frequency and different directions. The spectrum was derived from SWAN model at S9, for February, 4, 1979 at 23:00:00\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Fig1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/1a1ae4096f9c15b5dc1a6aae.jpg"},{"id":33232109,"identity":"f09e9d4e-ecf5-43b3-8fba-4c340d3fd18b","added_by":"auto","created_at":"2023-02-21 14:41:05","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1360248,"visible":true,"origin":"","legend":"\u003cp\u003eThe geographic positions of the analysed points.\u003c/p\u003e","description":"","filename":"Fig2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/a0fff1a4a37c13343cc7b38e.jpg"},{"id":33231163,"identity":"c257dafd-e8fe-4029-bd57-9de2e5f095f3","added_by":"auto","created_at":"2023-02-21 14:33:05","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2834032,"visible":true,"origin":"","legend":"\u003cp\u003eThe averaged directional wave spectra for the period 1979–2020 over the Black and Azov Seas.\u003c/p\u003e","description":"","filename":"Fig3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/7250aae96e5d414a724b6cfe.jpg"},{"id":33232113,"identity":"fd3c689f-a906-4347-aa87-b0dcc44808a7","added_by":"auto","created_at":"2023-02-21 14:41:06","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":4966278,"visible":true,"origin":"","legend":"\u003cp\u003eThe averaged directional wave spectra for each season for the period 1979–2020 over the Black and Azov Seas\u003c/p\u003e","description":"","filename":"Fig4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/8e5f254739c1ef33f8cfe70b.jpg"},{"id":33231172,"identity":"f98de2c0-ee68-4c23-9892-ce99c6259d97","added_by":"auto","created_at":"2023-02-21 14:33:06","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":12062250,"visible":true,"origin":"","legend":"\u003cp\u003eThe averaged directional wave spectra for each month for the period 1979–2020 over the Black and Azov Seas\u003c/p\u003e","description":"","filename":"Fig5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/ab0f4e95a9f35d8f681e9725.jpg"},{"id":33233072,"identity":"dae4b00b-0f35-4e7d-8b21-d9d4e637d183","added_by":"auto","created_at":"2023-02-21 14:49:06","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1973801,"visible":true,"origin":"","legend":"\u003cp\u003eThe frequencies of occurrence of the different sea states in terms of number of peaks estimated on a two-dimensional spectrum. The frequencies of occurrence are calculated over a 42 year period between 1979 and 2020 with a resolution of one hour between each two-dimensional spectrum. The total of 368 904 two-dimensional spectrum are considered.\u003c/p\u003e","description":"","filename":"Fig6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/2530d106884511740803058c.jpg"},{"id":33232111,"identity":"fe24a3a7-c5c3-4aac-9c21-1fbe0885d7a2","added_by":"auto","created_at":"2023-02-21 14:41:05","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2168158,"visible":true,"origin":"","legend":"\u003cp\u003eAverage variance density of the 1st, 2nd and 3rd peaks under different sea states in terms of number of peaks estimated on a two-dimensional spectrum. The averages in variance density are calculated over a 42 year period between 1979 and 2020 with a resolution of one hour between each two-dimensional spectrum. The total of 368 904 two-dimensional spectrum are considered.\u003c/p\u003e","description":"","filename":"Fig7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/43085a3e9bc8315e44092a09.jpg"},{"id":33231168,"identity":"6c347b31-690a-4704-b056-b19930fa041b","added_by":"auto","created_at":"2023-02-21 14:33:06","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2469764,"visible":true,"origin":"","legend":"\u003cp\u003eAveraged peak frequencies of the 1st, 2nd and 3rd peaks under different sea states in terms of number of peaks estimated on a two-dimensional spectrum. The averages in peak frequencies are calculated over a 42 year period between 1979 and 2020 with a resolution of one hour between each two-dimensional spectrum. The total of 368 904 two-dimensional spectrum are considered.\u003c/p\u003e","description":"","filename":"Fig8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/063eb45508fd7babb2edbb38.jpg"},{"id":33231165,"identity":"b2cb360c-a0a5-4f21-880d-c6305f0f137c","added_by":"auto","created_at":"2023-02-21 14:33:05","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":2168862,"visible":true,"origin":"","legend":"\u003cp\u003eAveraged direction of the 1st, 2nd and 3rd peaks under different sea states in terms of number of peaks estimated on a two-dimensional spectrum. The averages in direction of peaks are calculated over a 42 year period between 1979 and 2020 with a resolution of one hour between each two-dimensional spectrum. The total of 368 904 two-dimensional spectrum are considered.\u003c/p\u003e","description":"","filename":"Fig9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/3b89be79dc792ce8ade7c01b.jpg"},{"id":33232110,"identity":"373d57f1-9697-4498-ac15-e4cd6b6b7f27","added_by":"auto","created_at":"2023-02-21 14:41:05","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":5165966,"visible":true,"origin":"","legend":"\u003cp\u003eVariance density rose charts of the 1st, 2nd and 3rd peaks. The frequencies are calculated over a 42 year period between 1979 and 2020 with a resolution of one hour between each two-dimensional spectrum. The total of 368 904 two-dimensional spectrum are considered.\u003c/p\u003e","description":"","filename":"Fig10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/16efad70dd1c0d9707ee33cc.jpg"},{"id":34122993,"identity":"7939d24a-d79b-4daf-98ad-27a0a8b5ff2d","added_by":"auto","created_at":"2023-03-12 13:14:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2055085,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2596229/v1/4bbdffc3-bd36-425b-94d5-a579a5a270ba.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Long-term spectral wave climate in the Black Sea based on directional wave spectra","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eA thorough statistical understanding of the ocean wave environment is crucial for many scientific and engineering applications (Portilla-Yand\u0026uacute;n et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Sea conditions are a combined result of reactions from multiple wave systems, and the synthesis of these multiple wave systems produces the sea surface states. Only part of the resulting surface waves is aligned with the wind direction due to complex energy transfers from the atmosphere to the sea (Teixeira and Guedes Soares \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Wave climate analysis can be performed more efficiently by using wave spectra since the spectra provide more detailed information than the bulk wave parameters (Shimura and Mori \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), such as significant wave height (H\u003csub\u003em0\u003c/sub\u003e) and mean wave period (T\u003csub\u003em02\u003c/sub\u003e).\u003c/p\u003e \u003cp\u003eThe wave spectrum describes complex sea states in frequency and directional domains and provides a comprehensive representation of the existing wind-sea and swell wave combinations (Boukhanovsky and Guedes Soares \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Spectral partitioning of wave data can provide the scientific community with more detailed and comprehensive information (Albuquerque et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). For an accurate sea simulation, the directional wave spectrum constitutes the basis for investigating the interaction between waves and marine structures (Goda \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Additionally, for the design of ships and offshore structures, methods for assessing wave-induced stresses do not only require estimates of bulk wave parameters but also data on the directional spectrum of waves (Boukhanovsky et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). For instance, Considering changes in the bulk wave parameters fails to properly incorporate the existence of positive and negative variations in the wave climate within the directional spectrum (Lobeto et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The bulk parameters provide a good account of the wave characteristics in cases of uni-modal seas, but they fail to adequately represent the sea state in more complex situations (Lucas et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Portilla-Yand\u0026uacute;n et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Marine structures are subjected to all types of sea states that can occur during their lifetime, and it has been demonstrated that in many situations, the sea states are a result of the combination of more than one wave system, and in this case, the frequency spectrum exhibits two peaks (Teixeira and Guedes Soares \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), or more. The wave climate data are mainly treated as the long-term statistics of significant wave heights H\u003csub\u003em0\u003c/sub\u003e, mean periods T\u003csub\u003em02\u003c/sub\u003e and mean directions θ at the global ocean (Challenor et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Liang et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Smith et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Colosi et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) or regional scale (Kamranzad 2018; Vieira et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Young et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Sreelakshmi and Bhaskaran \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Amarouche et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHowever, in recent decades, the interest in wave climate studies based on directional wave spectrum has been raised (Portilla et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Hamilton \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Lucas et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Portilla-Yand\u0026uacute;n et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Vledder and Akpinar \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Jiang and Mu \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Jiang \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e); noting that directional spectra provide information that cannot be obtained from the commonly used method based on integrated wave parameters (Lobeto et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). According to (Toffoli et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), There are indications that wave trains traveling along different directions in general and crossing seas, in particular, should be seen as possibly dangerous conditions. The shipping and offshore industry are accounting for the situation of the combined sea in the design approach (Boukhanovsky et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe present study, therefore, aims to perform a long-term (42 years) spectral wave climate analysis for the Black and Azov seas. The long-term climatic wave spectra are evaluated by averaging the climatic distribution of spectral wave density as a function of frequency and direction on annual and seasonal scales. On the other hand, a spectral partitioning of individual waves was performed, and the long-term occurrence of mono-peak wave spectra (uni-modal seas), double-peak (bimodal), and multi peaks (multi-modal) wave spectra. The spectral partitioning was performed using an innovative approach presented by (Portilla et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Portilla-Yand\u0026uacute;n et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and initially applied in the Black Sea by (Vledder and Akpinar \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The approach consists of pre-processing the wave spectra using smoothing tools to follow the steepest ascending variance density path until a peak is reached and finally to merge all points climbing to the same local peak (Portilla et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). However, in the present study, the individual wave partition is studied based on the peak characteristics of all analyzed directional wave spectra. The corresponding frequency, direction, and energy of each peak are obtained from the no smoothed wave spectra. A relatively similar approach was adopted in previous studies (Hamilton \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Lucas et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Hamilton, (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) applied statistical sampling and clustering algorithms to classify the wave spectral shape observed in shallow water locations off northwest Australia and claimed that the classification and identification of distinct wave systems made it possible to describe wave spectral data sets more accurately without losing information. Thus, Lucas et al., (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) performed a classification of the wave spectra in North-eastern Atlantic and Portuguese coastal waters based on wave spectral shape. They proposed five classes of spectral wave systems based on the number of peaks and spectral shape characteristics. Bukhanovsky et al., (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) used the same approach proposed by (Lucas et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) in several locations around the world, including one location in the southern part of the Black sea and one in the Azov Sea. The spectral wave data used to perform the present study was developed using a SWAN (Simulating WAve Nearshore) model (Booij et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Ris et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). The model was spatially calibrated for the Black Sea and the Sea of Azov based on satellite altimeter and buoy measurements (Amarouche et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e), and validated against 14750 spectral measurements collected at the Utrish coast during a period of ~\u0026thinsp;11 months (Amarouche et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) because the model's accuracy in estimating the wave spectrum and an awareness of the model output uncertainty is critical for a reliable assessment of the spectral wave climate.\u003c/p\u003e"},{"header":"2. Material And Methods","content":"\u003cp\u003eConsidering the importance of the spectral wave climate in offshore and coastal activities, we strongly support the statement of Boukhanovsky et al., (\u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e) that it is now crucial to promote the development of more complete wave data atlases that incorporate spectral wave climate descriptions. The present study consists of a detailed assessment of long-term spectral wave climate in the Black and Azov Seas. For this purpose, hourly directional wave spectra for a period of 42 years between 1979 and 2020 were analyzed. Two widely used approaches are considered for processing the directional wave spectra. The first approach consists of averaging wave variance densities over the frequency and direction for annual and seasonal scales by considering the whole data set. According to Lucas et al., (\u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e), the computed results based on this first approach allow us to determine the climatic wave spectrum, initially termed by Buckley (\u003cspan class=\"CitationRef\"\u003e1988\u003c/span\u003e). This simple approach in analyzing the long-term climatic wave spectra was used in several previous studies, e.g. (Panigrahi and Swain \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Corbella and Stretch \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e; Espindola and Ara\u0026uacute;jo \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e; Patra et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The second used approach consists of a detailed assessment of the different wave systems occurring in the Back Sea and the Sea of Azov, including the uni-modal and multi-modal wave systems. This approach consists in partitioning the individual wave system observed in each directional wave spectra to determine the number of wave systems by referring to the independent spectral peak at each observation, followed by a classification of the observed sea states during the analyzed period, to determine the occurrence of uni-modal and diferentes multi-modal wave systems. Furthermore, the peak energy, peak frequency, and peak direction of the first three spectral wave partitions are deeply evaluated. The analyses are performed on 25 selected locations shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e provides further information about the depth at each location and their distance to the coastal line. The methodology used to process the different wave systems based on the shapes of the directional wave spectra by clustering the mono and multi-peak wave system was recently used by several researchers to study the spectral wave climate at different locations around the world, e.g. (Hamilton \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Lucas et al. \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e; Bukhanovsky et al. \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Portilla-Yand\u0026uacute;n et al. \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"char\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eThe geographic charachteristics of 25 selected reference locations\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eStation nbr\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eLon\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eLat\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDepth (m)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eDistance from the coastal line ( ˚)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"25\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eSelected locations\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-12.0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.501\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e37.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e46\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-10.3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.347\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd 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char=\".\"\u003e\n\u003cp\u003e0.000\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e29\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-79\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.393\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1356\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.924\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS10\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e33\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2156\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.110\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS11\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e35\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2205\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.234\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS12\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e37\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2111\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.288\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e43.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2038\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.520\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e28\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-49\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.224\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e30\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2164\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.308\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e32\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2204\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.830\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e34\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2050\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.518\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e36\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1946\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.766\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e38\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-2146\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1.400\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e40\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e42.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1839\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.731\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS21\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e29\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-111\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.241\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS22\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e31\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1279\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.423\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS23\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e37\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-199\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.201\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS24\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1976\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.451\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eS25\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e41.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e-1501\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.266\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTo summarise, the whole study was performed in four main steps, i. calibration of the model and evaluation of its accuracy in estimating wave spectra (Amarouche et al., \u003cspan class=\"CitationRef\"\u003e2021b\u003c/span\u003e). ii. development of a long-term wave hindcast derived from the calibrated and validated model. iii, partitioning of the wave spectrum performed based on two-dimensional wave spectra. iv. long-term statistical analysis of wave spectral data considering each wave system in 25 sites in the Black Sea and the Sea of Azov. In the following section, we provide more detailed information on the used model, the used data accuracy, and the spectral partitioning and processing method.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003e2.1. Development of the spectral wave database\u003c/h2\u003e\n\u003cp\u003eAt present, the only way to obtain a piece of long-term information on directional spectral wave climate is through the use of spectral wind-wave models. The buoy and radar-measured wave spectra can only serve for a limited period and at limited sea locations. To perform this study, a long-term database of a 42 years\u0026rsquo; period was developed using a calibrated model SWAN with a time resolution of 1h. The SWAN model was calibrated at a spatial scale based on satellite observation to ensure a balanced accuracy over the whole basin. The spatial calibration allows an accurate evaluation of the spatial variability in the wave climate, even in the location in gaps of buoy measurements. The SWAN model calibration reduces the underestimations of wave energy observed by considering the default model setting in the Black Sea as documented in previous studies (Moeini and Etemad-Shahidi \u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e; Kamranzad et al. 2013; Rascle and Ardhuin \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Akpınar et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Akpinar and Ponce de Le\u0026oacute;n \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Atan et al. \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e; Kutupoğlu et al. \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e; Bing\u0026ouml;lbali et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The model is calibrated after a sensitivity test to the used wind and whitecapping source terms and to the used wind forces. Thus, the tuneable coefficient (C\u003csub\u003eds\u003c/sub\u003e) which is related to the wave dissipation by whitecapping, was tuned to obtain an optimal value. The calibrated SWAN model was run in non-stationary mode with a simulation time-step set to 30 min. The wind and whitecapping source term of Komen \u003cem\u003eet al.\u003c/em\u003e, (1984) was chosen based on the calibration results. The C\u003csub\u003eds\u003c/sub\u003e coefficient value is set at 0.8\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e. The JONSWAP (Hasselmann et al. \u003cspan class=\"CitationRef\"\u003e1973\u003c/span\u003e) shape of the spectra in both frequency and direction is used with a gamma ray peak enhancement parameter of 3.3. The directional wave energy density spectrum is discretized with a constant increment of 35 bins for the frequencies ranging between 0.04 Hz and 0.625 Hz and 36 bins for the spectral wave directions. The ERA5 reanalysis wind (Hersbach et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) was used to force the model for the whole simulated period. ERA5 data were developed by the European Centre for Medium-Range Weather Forecasts (ECMWF) and provided by the Copernicus Climate Change Service (C3S) Climate Data Store \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cds.climate.copernicus.eu/\u003c/span\u003e\u003c/span\u003e (last accessed in 15.06.2021). The ERA5 wind data are characterized by a spatial resolution of 0.25\u0026deg; \u0026times; 0.25\u0026deg; and cover the period from 1979 to the present. The ERA5 wind is considered the most accurate wind forcing for wave modelling in the Black sea based on the results obtained in previous studies (Van Vledder and Akpinar \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e; \u0026Ccedil;alışır et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Amarouche et al. \u003cspan class=\"CitationRef\"\u003e2021b\u003c/span\u003e; Soran et al. \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e), which used and compared different wind reanalysis. Thus the accuracy of the ERA5 wind reanalysis was shown in several other studies at different seas (Baordo et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Sharmar and Markina \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Beyramzadeh et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Amarouche and Akpınar \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eConcerning the computation grid, an unstructured mesh grid was used. This grid is developed using OceanMesh2D 1.0 (Roberts et al. \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The spatial resolution is 300m in the nearshore and increasing gradually to 11km in the offshore. This grid covers all the Black Sea and Azov Sea and the model output are obtained for all grid points for a period of 42 years and a time resolution of 1 hour. The developed data base contains both directional and non-directional spectral data, managed in yearly NetCDF folders.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n\u003ch2\u003e2.2. Spectral data accuracy and uncertainty\u003c/h2\u003e\n\u003cp\u003eThe evaluation of spectral wave model precision in the estimation of directional wave spectrum is rarely documented. In general, wave models are evaluated based on wave parameters such as H\u003csub\u003em0\u003c/sub\u003e and T\u003csub\u003em0\u003c/sub\u003e and the mean direction, but the accuracy of the spectral energy distribution as a function of frequency and direction is usually not considered. The accuracy of the model in estimating H\u003csub\u003em0\u003c/sub\u003e may reflect a good accuracy in the total energy spectrum of the bi-modal waves, but it can never indicate accuracy in the spectrum as a function of the frequency, direction, and energy of the peaks, nor accuracy in the multi-modal energy spectrum. The wave model used for developing the directional wave spectra hindcast data is evaluated by (Amarouche et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) based on 14,710 spectral measurements collected over about 11 months on the Utrish coast using a Datawell DWRG-4. Uncertainties related to the spectral wave model are discussed in (Amarouche et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) in terms of the annual and seasonal averaging and also in estimating the individual spectrum shapes. The average wave spectra estimated by the SWAN model show a good accuracy compared to the measurements, with a slight overestimation of ~\u0026thinsp;10% in spectral energy between 0.13 and 0.17 Hz. In terms of spectral direction, a maximum bias of 20 degrees is observed. It should be noted that the measurement buoy is located very close to the coast at a depth of 42m within a complex bathymetric zone. In terms of the model's accuracy in estimating individual spectrum shapes, the statistical errors showed a correlation greater than 0.7 for the frequency range from 0.08 Hz to 0.5Hz and exceeding 0.8 in a range of high spectral frequency (0.15\u0026ndash;0.32 Hz) in the Utrish buoy. In addition, it should be noted that the frequency-based RMSE results are more pronounced between 0.1Hz and 0.17Hz, with a maximum RMSE of 0.09 m\u003csup\u003e2\u003c/sup\u003e/Hz.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e2.3. Spectral wave partition and processing approach\u003c/h2\u003e\n\u003cp\u003eThe long-term spectral wave climate assessment is a complex process due to the significant quantity of information contained in one spectral measurement. Directional wave spectra may provide information on real sea states. It provides information on the individual wave systems and allows us to define the different wind-sea, and swell partitions. The partitions contained in each spectrum can be characterized by a peak direction, a peak frequency, and a peak energy. By determining the different partitions of the estimated wave spectra, statistical analysis of the wave spectral systems over a long period may provide deep information on the spectral wave climate in the Black and Azov Seas. Thus, by averaging the spectral variance density as a function of time, frequency, and direction, we can determine a climatic wave spectrum as defined by (Buckley \u003cspan class=\"CitationRef\"\u003e1988\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eSeveral operational methods are proposed for spectral wave partitioning. Some methods can permit the separation of the wind sea from the swell partition, and others allow the determination of more than two partitions in the case of multi-modal wave systems. The most straightforward proposed approach to spare the wind sea from the swell is to set a partition frequency value to separate the low-frequency waves (swell) and the high-frequency waves (wind sea). Among the empirical approach used to define the partition frequency value f\u003csub\u003epar\u003c/sub\u003e, we can note the Earle (1984) approach. The latter is based on the frequency spectrum of Pierson and Moskowitz forced by the local wind speed and can be approximated as follow (Earle 1984):\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$${f}_{par}=0.8\\times {f}_{PM}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$${f}_{PM}=0.13\\times \\frac{g}{{U}_{10}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere f\u003csub\u003ePM\u003c/sub\u003e denotes the peak frequency of the Pierson and Moskowitz spectrum in a fully developed wind wave (Pierson and Moskowitz \u003cspan class=\"CitationRef\"\u003e1964\u003c/span\u003e), g is the gravity acceleration, and U\u003csub\u003e10\u003c/sub\u003e is the wind speed at 10m above the sea surface.\u003c/p\u003e\n\u003cp\u003eThe partition frequency can also be determined without wind information by considering the wave steepness proposed by (Wang and Hwang \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e). In these approaches, the wind sea and swell are distinguished by a separation frequency value derived from the peak frequency of the steepness function based on the Pierson\u0026ndash;Moskowitz spectrum (Wang and Hwang, \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e). Those partitioning methods are operational. However, they only allow us to separate the wind sea from the swell and do not allow us to determine all wave partitions in case of a multi-modal wave system or multi-peak spectrum. To divide all probable wave partitions, Gerling (\u003cspan class=\"CitationRef\"\u003e1992\u003c/span\u003e), proposed a 2d partition scheme using the directional wave spectra. He proposed an algorithm allowing wave spectral partition in terms of frequency and direction. Following the same approach proposed by Gerling (\u003cspan class=\"CitationRef\"\u003e1992\u003c/span\u003e), (Hasselmann et al. \u003cspan class=\"CitationRef\"\u003e1996\u003c/span\u003e) and (Hanson and Phillips \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) developed and used another improved algorithm. (Hasselmann et al. \u003cspan class=\"CitationRef\"\u003e1996\u003c/span\u003e) applied the approach for the partition of two-dimensional wave spectra obtained from the synthetic aperture radar (SAR) image spectra, and (Hanson and Phillips \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) proposed another algorithm as an automatic Wave Identification and Tracking System (WITS). The partition scheme of (Hanson and Phillips \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) consists in isolating the peaks in the spectral direction and to combine the wind-sea peaks based on the wave age criterion. The wave age criterion is defined as\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"\" /\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAnd in the deep water\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$${f}_{p}\\ge \\frac{g}{2\\pi }{\\left[{C}_{wind}\\times {U}_{10} \\times \\text{cos}\\left({\\theta }_{W}- {\\theta }_{WS}\\right)\\right]}^{-1}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn which c\u003csub\u003ep\u003c/sub\u003e is the wind sea's phase speed at a particular peak frequency, C\u003csub\u003ewind\u003c/sub\u003e is a tuneable factor in guaranteeing all potential wind sea peaks are considered. \u0026theta;\u003csub\u003ew\u003c/sub\u003e and \u0026theta;\u003csub\u003ews\u003c/sub\u003e refer to wind direction and wind-sea direction successively. As a result, the first partition is formed by combining the partitions whose peak fits these requirements and classifying them as wind seas.\u003c/p\u003e\n\u003cp\u003eIn the case of multi peaks spectra, (Hanson and Phillips \u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) algorithm first determines the swell peaks and then combines the adjacent swell peaks as mutual swell belonging to the same swell system. These methods permit the identification of all different partitions as a function of their frequency and direction in the multi-peak wave spectra.\u003c/p\u003e\n\u003cp\u003eReferring to the idea initiated by Gerling, (\u003cspan class=\"CitationRef\"\u003e1992\u003c/span\u003e), Portilla et al., (\u003cspan class=\"CitationRef\"\u003e2009\u003c/span\u003e) proposed an improved operational approach in which the wave spectra are pre-possessed using a smoothing tool as noise-removal in a two-dimensional scale. By the next, based on the smoothed wave spectra, the steepest ascending variance density paths are followed until the peak, and all points connected to the same peak are grouped as an individual wave partition. Based on the same idea, the peak locations of each individual wave system are located. Noting that the presented study focuses on the spectral wave climate in the whole Black and Azov Seas, and not in one location, the number of information is significantly high for 42 years. The present study is mainly focused on the occurrence of the different waves system, and the peak characteristics of each individual partition are statistically analysed in terms of their frequency, direction, and energy. The plot in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows an example of the results obtained by partitioning directional wave spectra and identifying the peaks at each partition and their characteristics.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe different combined sea states are classified based on the number of the wave system in 5 classes, considering the wave spectra with one wave system (mono peak) and those of 2 to 5 wave systems (multi-peak). The partition order of each wave spectra is determined based on their peak energy from the most energetic (partition 1) to the least energetic. The total number of the directional wave spectra is 368,196 for a period of 42 years and a time resolution of 1h, for a total of 23 offshore locations over the Black Sea and 2 stations in the Sea of Azov are considered for the evaluation of the spatial variability in the spectral wave climate.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results And Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Long-term average wave spectra\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe analysis of two-dimensional spectral data provides a better understanding and better characterization of the wave climate behavior in the Black Sea and the Sea of Azov. The hourly 2D wave variance densities (wave spectra) (in frequency and direction domain) were averaged and visualized on annual, seasonal and monthly basis at 25 selected offshore stations (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), representing different regions of the Black Sea and Sea of Azov. The results are showed in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Two-dimensional intensity spectra are used to identify the main wave peaks according to their direction and frequency. The lower averaged values of the spectral variance density with an energy above 0.01m\u003csup\u003e2\u003c/sup\u003e/Hz are neglected and not ploted to better observe changes focusing on the most occuring and most energetic wave systems.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe mean variance density calculated for a period of 42 years (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) shows that only the southwestern Black Sea (location A21) and southeastern Black Sea (location A25) regions are characterized by a single main averaged density peak of (\u0026gt;\u0026thinsp;0.2m\u003csup\u003e2\u003c/sup\u003e/Hz), while in the rest of the Black Sea the wave spectrum shows an occurrence of multiple averaged density peaks ranging from two to three peaks (\u0026gt;\u0026thinsp;0.2m\u003csup\u003e2\u003c/sup\u003e/Hz). The directional spectrum of the waves in the eastern part of the Black Sea shows the occurrence of two opposite and energitic (\u0026gt;\u0026thinsp;0.05m\u003csup\u003e2\u003c/sup\u003e/Hz) spectral density peaks (S13, S19, S20, S23, and S24). The peaks formed by the waves traveling eastward in this region have higher frequencies. This reflects the presence of wind waves from northeast to southeast. In the center of the Black Sea (locations S10, S11, S17) the spectral density plots show multiple peaks density (\u0026gt;\u0026thinsp;0.2m\u003csup\u003e2\u003c/sup\u003e/Hz) from different directions and frequencies. The Northeast and Northwest peaks are located at high frequencies, while the Southwest and Southeast peaks are located at lower frequencies. Moreover, no southern spectral density with an average value above 0.01m\u003csup\u003e2\u003c/sup\u003e/Hz was observed in the center of the Black Sea. In the northwestern part of the Black Sea (locations S3 - S5 and S9) spectral peaks are multiple. The Northern and Northeastern and eastern wave peaks have high intensity and low frequencies, while the West to Southwest wave peaks have lower intensity and higher frequencies. In the Northeast Black Sea (locations S6 and S7), the wave spectrum shows the presence of two main peaks, the more intense peak is from West to Southwest and the second peak is from East to Southeast. In the eastern Sea of Azov (location S2), the spectrum shows the presence of three main peaks with a frequency of about 0.2 Hz from the North-Northeast-Southeast and South-Southwest directions. In the western Sea of Azov (location A1), two opposed peaks with low intensity and low frequency of 2.5 Hz are observed in the East-Northeast and West-Southwest directions. Those peaks reflects a dominance in wind sea at this region. In terms of wave intensity, the Western and Southwestern part of the Black Sea is characterized by the highest spectral intensity from Northeastern and Eastern origin, where the mean intensity variance reaches 0.4 m\u003csup\u003e2\u003c/sup\u003e/Hz. Thus, the wave intensity observed in the center is concentrated in the directions from Northeast and Northwest to West.\u003c/p\u003e \u003cp\u003eOn a seasonal scale (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e), there is clearly a seasonal variability in the spectral density distribution as a function of wave direction and in terms of the main peak number and variance density values. During the winter period, a wave peak distribution similar to the values observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for the annual average is observed in term of direction. However, the averaged densities peaks are located in a lower frequency and mainly around 0.1Hz, reflecting the intensity of the swell during the winter. Another exception appears for the station located southwest of the Black Sea near the Bosphorus (location S21), where a southwest peak at a low frequency of ~\u0026thinsp;0.25 Hz and a variance density of ~\u0026thinsp;0.04m\u003csup\u003e2\u003c/sup\u003e/Hz appear. This peak reflects the exceptional wind-sea activity in that location (S21) during the winter. The averaged variance density reached 0.7 m\u003csup\u003e2\u003c/sup\u003e/Hz for the multiple peaks observed in the western part of the Black Sea (locations S4, S5, S8-S10, S15, and S16) in the winter. Moreover, this maximum intensity is observed in the spectrum of double main peaks in the center (locations S10, S11, and S17), while in the eastern region the spectral intensity is lower and the peaks are generally more pronounced from the Southwest, West and Northeast directions (locations S13, S19, S20, S23, S24, and S25). In the Sea of Azov (locations S1 and S2), the eastern region is more energetic, with the presence of three to four main peaks in different directions; Southwest, Southeast, EastNortheast and NorthNortheast. On the other hand, the western part of the Sea of Azov has lower intensity and three peaks from the Southwest, West and Northeast directions. During the spring, the wave spectrum shows a lower density of high frequency waves. Moreover, the seasonal average variance density is very close to the annual average variance density presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Moreover, in the spring, the Northeast and East variance intensity values in the eastern part of the Sea of Azov (location S1) and northeast of the Black Sea (locations S6 and S7) are more consistent with the annual average. In summer, the wave spectrum shapes mostly show a single peak in the eastern and western Black Sea and two peaks in the center, except in the eastern Sea of Azov (location S2), where three peaks with low intensity are observed. The southern coast of the Black Sea is exposed to more energy during the summer months compared to the northern coast. During the autumn, in the western and eastern parts of the Black Sea, the wave spectra are very similar to those observed in spring and to the annual average. In the northeastern part of the Black Sea (locations S6 and S7) and in the eastern part of the Sea of Azov (location S1), the variance of the mean intensity from the Northeast direction is greater in autumn than in spring.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOn a monthly scale (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003ea to \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003ec), the average spectral wave regime shows that four different wave patterns occur throughout the year. It is noteworthy that the months of November, December, January, February and March present a spectral pattern with the same number of peaks and a very similar range of variance intensity in the Black Sea, while in the Sea of Azov there is no similarity. April, May and June show a similar spectral wave pattern with lower variance intensity. July and August are the two calmest months. During these two months, wave spectral patterns are generally single-peaked along the southern coast (locations S21 - S25) and eastern part (locations S13, S19, and S20) and double-peaked in the rest of the Black Sea and the Sea of Azov. September and October shows the same spectral regime in the northern part of the Black Sea, while in the eastern part, the shape of the wave spectrum during October is different. In October, low-frequency waves can be observed moving from the East to the Southeast. These results show a different classification of the seasons in terms of wave spectral regime. The results for winter are similar to those for November, December, January, February, and March. The results obtained for the spring are more similar to April, May, and June, while the results for summer are more reflective of July and August. Finally, the results for the autumn are more comparable to September and October, except for the eastern part of the Black Sea.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Occurrences of unimodal and multi-modal sea states\u003c/h2\u003e \u003cp\u003eThe individual wave system partitions at each directional wave spectra are identified and characterized based on peak density, frequency, and direction. The number of individual wave systems along the hourly time series are computed for each wave spectra. The obtained results allowed as to determine the occurrences in percent of the unimodal and multi-modal sea states around the Black Sea and the Sea of Azov (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The results show a low occurrence of unimodal sea states at most regions of the Black Sea (the locations S3-S13, S15-S20, S22, and S24). The occurrences of the unimodal sea states varied between 7% and 19%. However, in the Sea of Azov, the occurrences in unimodal sea states are more important, with 48% in the west and 51% in the east. Four other locations in the Black Sea (the locations S14, S21, S23, and S25) are also dominated by unimodal sea state and located on the south-eastern and the south-western coasts of the Black Sea. The unimodal occurrences at those locations varied between 36% and 40%. The bi-modal sea state shows a high occurrence at all locations at both the Black Sea and the Sea of Azov, with a minimum occurrence of 23% in the eastern part of the Azov Sea and the western part of the Crimean Peninsula and a maximum of 36% off the central coast of Turkey. The tri-modal sea states are highly occurring in the most of Black sea (the locations S14, S21, S23, and S25). With 24\u0026ndash;32% of the total sea states, except in the Black Sea's south-western and south-eastern coasts, the maximum occurrence of the tri-modal wave system is 17%. Thus, the occurrence of a tri-modal wave system in the Azov Sea is lower and varies between 12% in the east and 14% in the west. The occurrence distributions of the quad-modal and quint-modal sea states follow the distribution of the tri-modal sea state with lower abundance. The quad-modal and quint-modal sea states are more occurring in the Black Sea's offshore locations (S5, S9 - S12, and S16). In the Sea of Azov, the sea states with more than three individual wave systems are less than 8%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Characteristics of spectral wave systems\u003c/h2\u003e \u003cp\u003eThe characteristics of individual wave systems partitions at all wave spectra are defined considering their number and the peak density, frequency, and direction of each individual wave system. Based on the number of wave systems in the directional wave spectra, the sea conditions are defined as unimodal or multi-modal. It was noticed that the multi-modal sea states are more dominant in the Black Sea (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). However, the information on occurrence of the individual sea states should be completed by the character of each wave system at different sea state conditions. The occurrences of multi-modal sea states in a specific location do not necessarily reflect a higher energy distribution. For instance, the results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e show that the averaged densities of the prominent peaks (1st peaks) are more critical during the unimodal sea state events in the Azov Sea (the locations S1 and S2) and at most of the Black sea (the locations S3-S8, S10, S12-S15, S18-S21, S24-S25). In those locations, the average densities of the prominent peaks of all wave spectra containing one individual wave system are more important compared to the average density of the main peaks in a wave spectrum containing two or more wave systems. However, an exception is observed at four locations (S9, S11, S17, and S22) where the averaged densities of the first main peak are more important in the case of bi-modal sea states and even with tri-modal sea states at location S22. With the increase in the number of individual wave systems, the average density of the primary peak generally decreases. We can conclude that the maximum peak energy in the Azov Sea and a large part of the Black Sea can be more interesting to study during the unimodal wave sea states. The information on the spectral peak density is important for evaluating the fatigue life of marine structures (Zeinoddini et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). The highest average in peak density exceeding 2 m\u003csup\u003e2\u003c/sup\u003e/Hz is observed in the Black Sea's south-western basin.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eConcerning the average density of the 2nd main peak, we can also notice a dependence on the sea state conditions and the number of individual wave systems. The averaged density of the 2nd main peak is more critical at the locations S1 - S3, S7, S8, S14, S15, S21, and S24 but is more important during the tri-modal wave system at the remaining locations. The average density at the 2nd peak is less important during the quad-modal and quint-modal sea states. The highest density of the 2nd main peaks in the 2d wave spectrum is observed in the western Black Sea basin. The average density of the 2nd peak in the Azov Sea does not reach 0.2m\u003csup\u003e2\u003c/sup\u003e/Hz. The 3rd main peak averaged density in the wave spectrum is neglected at the Sea of Azov and significantly low in the Black Sea. The average density of the 3rd peak is more important during the quad-modal and quint-modal sea states except at the locations S7 and S21, where the averaged density is more important for the tri-modal sea states.\u003c/p\u003e \u003cp\u003eLooking at the results of the peak frequency average (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) computed for the prominent three peaks and during different sea state conditions, we noticed that the frequency of the 1st peak is lower compared to the 2nd peak frequency, which is slightly lower compared to the 3rd peak frequency. Thus, we can notice a dependence of the peak frequency on the number of individual wave systems. At most locations, the 1st, 2\u003csup\u003end,\u003c/sup\u003e and 3rd peak frequency averages increase by increasing the number of individual wave systems. However, an exception for the 1st peak frequency averages is observed at the locations S13, S20, and S22. In locations S13 and S20, the frequency of the 1st peak during the bi-modal sea states is lowered. In the location S22, the frequency of the 1st peak during the unimodal sea state is higher than all 1st peak frequency averages in multi-modal sea states. The same finding is observed at the locations S13, S20, and S24, comparing the averaged frequency of the 2nd peak and 3rd peak during the bi-modal and tri-modal sea states successively to their frequency in the presence of more individual wave systems. Based on those results, we found that the highest peak energy and the lowest frequency occur during the unimodal sea states in the most of the Black Sea. High peak density at low frequency can reflect a concentred amount of energy which can be dangerous for marine structures.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRegarding results of averaged peak direction of the main three peaks (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) computed for the different sea state systems, we can notice a clear dependence of the spectral peak means direction to the number of wave systems. The mean directions of the 1st main peak during the unimodal sea states are largely different from the mean directions of the 1st main peak during the multi-modal sea states. The differences can exceed 30ͦ at most locations depending on the number of wave systems. The same situation is observed for the 2\u003csup\u003end,\u003c/sup\u003e and the 3rd peaks' mean directions. The mean peak direction changes remarkably depending on the number of wave systems. These results reflect that different climate patterns govern the various individual wave systems. Evaluating the possible connection of the individual wave system to the distinct climate patterns anomaly may provide a better understanding of wave climate in the Black Sea. At the location S5, we can observe the highest difference of \u0026gt;\u0026thinsp;75ͦ between the 1st peak mean direction computed during the unimodal sea states and the 1st peak mean direction computed during the multi-modal sea states systems. Considerable differences are also observed between the 2nd and 3rd peak directions at different sea systems. It is important to notice that the averaged direction will depend more on each wave system's most occurring direction. Thus, the averaged direction does not necessarily provide accurate information about the individual wave system direction if the dominated waves originated from two or more dominated directions. Thereby, in the following section, we are presenting the occurrences of the first three peaks in the directional wave spectra as a function of directions, densities, and frequencies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Occurrences of individual wave system\u003c/h2\u003e \u003cp\u003eBased on individual wave systems; characterized by their peak variance density and peak direction, the occurrences of the first main peaks are estimated as a function of directions. The results are presented using wave roses for 25 locations in the Black and Azov Seas (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e). The results show a considerable difference in the directional distribution of the 1st, 2nd, and 3rd peaks. The variation in peak direction is less important for the first wave system peak of the wave spectrums. The 1st peak mainly originated from two dominant directions in offshore locations or one dominant direction in the locations close to the coastal line. However, the 2nd and 3rd peaks of the wave spectra can be originated from a wider direction range. Three to four dominant directions of the 2nd and 3rd peaks can appear in the offshore locations. The main differences we can notice regarding the distribution of individual spectral peaks as a function of direction can be observed in the western part of the Black Sea (the locations S12, S13, S19, S20, and S25), where the 2nd peaks in the wave spectra are highly occurring from a western sector contrarily to the 1st peaks which are rarely occurring from the Eastern origin. In the western location S1 of the Azov Sea and the Odessa shelf (the location S3), the directions of the 1st peaks from the North sector are rare. However, the occurrence of the 2nd peaks originating from the North are more considerable. On the south-western coast of the Black sea (the location S22), we noticed a high occurrence of wave spectra with the 2nd peak of south-west origin, while similar directions for the 1st peaks in the wave spectra are rare in the same location.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eConcerning the distribution in spectral peak densities as a function of wave directions, we can notice that peak density exceeds 2m\u003csup\u003e2\u003c/sup\u003e/Hz from mostly all occurring directions and at all locations. The 1st peaks of \u0026gt;\u0026thinsp;0.5m\u003csup\u003e2\u003c/sup\u003e/Hz constitute\u0026thinsp;~\u0026thinsp;50% of the total occurring waves at most locations. The variance density exceeding 5m\u003csup\u003e2\u003c/sup\u003e/Hz is also observed in all Black Sea regions and the eastern location of the Azov Sea, however, with a low rate and mainly from the most dominated directions. For the 2nd peaks, the variance densities are lower, while the 2nd peaks in wave spectra with a variance density\u0026thinsp;\u0026gt;\u0026thinsp;0.5m\u003csup\u003e2\u003c/sup\u003e/Hz are considerably occurring at mostly all locations except at S1, S3, and S25. The 2nd peak with a spectral density\u0026thinsp;\u0026gt;\u0026thinsp;2m\u003csup\u003e2\u003c/sup\u003e/Hz also occurred in the western and central basins of the Back Sea and in the eastern location of the Azov Sea. Regarding the density of the 3rd peak in the spectrum, the peak densities rarely exceed 0.5m\u003csup\u003e2\u003c/sup\u003e/Hz. Thus, mostly the spectral densities of the 3rd peaks in the wave spectra are \u0026lt;\u0026thinsp;0.1m\u003csup\u003e2\u003c/sup\u003e/Hz. The locations experiencing events with a 3rd peak density\u0026thinsp;\u0026gt;\u0026thinsp;2 m\u003csup\u003e2\u003c/sup\u003e/Hz are S5 and S9.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Summary And Conclusions","content":"\u003cp\u003eThis study performed a long-term assessment of spectral wave climate based on hindcasted two-dimensional wave spectrum data in the Black and Azov Seas. The directional wave spectra are evaluated by averaging the climatic distribution of spectral wave density for each frequency and directional range. The annual, seasonal, and monthly wave spectral averages are computed and mapped for 25 grid locations. The individual wave systems was identified for each directional wave spectra. The unimodal and multi-modal sea states are filtered and occurrence of each sea states systems was defined. Considering the individual wave systems\u0026rsquo; peak caracteristics, long term averaged density, frequency and directions of the three first prominent individual wave system peaks are computed as a function of the sea state conditions. Finally, occurrences of the peak directions of the main individual wave systems at all directional wave spectra was computed as function of the spectral peak density.\u003c/p\u003e \u003cp\u003eThe obtained results, allow to describe with further details the wave climate of the Black and Azov Seas. The longterm averages of the variance densities in directional wave spectra at annual, seasonal and monthly scales allow us to define the locations of density peaks as a function of direction and frequency. Most locations in the Black Sea and Azov Sea are characterised by two or more critical peaks from different directions and frequency. According to this evidence, the long-term study of wave climate based only on bulk parameter H\u003csub\u003es\u003c/sub\u003e and mean period and mean directions is not sufficient to describe the wave climate regime in the Black and Azov Seas. For instance, if the wave density spectrum is consentrated at two or more directional ranges, the computed mean wave directions of the mixed sea my provide a wrong information.\u003c/p\u003e \u003cp\u003eThe occurrences of unimodal and multi-modal sea states showed that multi-modal spectra are more occurring, however, referring to the average density and frequency of the main wave system peak during the unimodal sea states, we noticed a highest peak density values and lower peak frequency at most location comparing to the main peak density values observed for multi-modal sea states. An exception was noticed at (S9, S11, S17, and S22), where the highest value in the averaged densities and the lower peak frequency in the 1st peaks are more observed during the bi-modal sea states. The spectral peaks\u0026rsquo; densities, frequencies and directions are depending on both the number of wave systems in the wave spectra and to the geographical location. We concluded that a multi-modal sea state in a specific location do not necessarily reflect a higher energy in the total wave spectra, and that unimodal sea states may contain more concentrated energy with low frequency in several locations (e.g. S8, S14, S15, and S22).\u003c/p\u003e \u003cp\u003eThe occurrences of peaks density of the individual wave systems as a function of directions presented using the individual wave system peak density roses allowed us to conclude that the 1st peaks in the wave spectra are mainly originated from two dominant directions and that ~\u0026thinsp;54% of the peaks\u0026rsquo; densities exceed 2 m\u003csup\u003e2\u003c/sup\u003e/Hz. However, the 2nd and 3rd peak in wave spectra are occurring from 3 or more dominant directions and the rarely exceeding the 2 m\u003csup\u003e2\u003c/sup\u003e/Hz.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 119N480. The authors acknowledge the European Center for Medium-Range Weather Forecasts (ECMWF) for providing ERA5 wind data through the Copernicus Climate Change Service (C3S) Climate Date Store. We also acknowledge the General Bathymetric Chart of the Oceans (GEBCO, www.gebco.net) for providing the bathymetry data.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under grant number 119N480.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Khalid Amarouche. The first version of the manuscript was written by Khalid Amarouche and edited by Adem Akpinar. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated during and/or analyzed during the current study are not publicly available at this stage, but are available from the authors on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkpinar A, Ponce de Le\u0026oacute;n S (2016) An assessment of the wind re-analyses in the modelling of an extreme sea state in the Black Sea. 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J Phys Oceanogr 49:543\u0026ndash;559. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1175/JPO-D-18-0149.1\u003c/span\u003e\u003cspan address=\"10.1175/JPO-D-18-0149.1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Directional wave spectra, Spectral wave climate, spectral partition, wind-wave, multi-peak wave spectra, individual wave systems. ","lastPublishedDoi":"10.21203/rs.3.rs-2596229/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2596229/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDirectional wave spectra describe complex sea states in frequency and directional domains and provide more detailed information than the bulk wave parameters. Spectral wave informations are important for the design of ships and offshore structures. Using hourly directional wave spectra hindcasted for a period of 42 years between 1979 and 2020, long-term spectral wave climate in the Black and Azov Seas was assessed. To determine the climatic wave spectrum, variance densities are averaged over the frequencies and directions for annual and seasonal, monthy scales. Futhermore, The individual wave system observed in each directional wave spectra are determined referring to the independent spectral peak at each observation. The different sea states conditions, including the uni-modal and multi-modal wave systems are classified and analysed; The energy, frequency, and direction of the three first prominent individual wave system peaks are deeply evaluated as a function of the sea state conditions. Occurrences as foction of spectral peak density and directions of the prominent individual wave system peaks are also computed and discussed. The results reveal that multi-modal spectra are more frequent in most regions, although the highest peak density values and lowest peak frequencies were observed within the wave spectra of uni-modal sea states. The spectral peak densities, frequencies, and directions depend both on the number of wave systems in the wave spectrum and on the geographic location. The first peaks in the wave spectra are mostly derived from two dominant directions and ~\u0026thinsp;54% of the peaks had a density greater than 2 m2/Hz. In contrast, the second and third peaks in the wave spectra are typically derived from three or more dominant directions and rarely exceed a density of 2 m2/Hz.\u003c/p\u003e","manuscriptTitle":"Long-term spectral wave climate in the Black Sea based on directional wave spectra","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-02-21 14:33:00","doi":"10.21203/rs.3.rs-2596229/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"17299961-5f99-4fb0-b243-9783f8784f92","owner":[],"postedDate":"February 21st, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-03-12T13:14:19+00:00","versionOfRecord":[],"versionCreatedAt":"2023-02-21 14:33:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2596229","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2596229","identity":"rs-2596229","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}