This section describes the intra-annual variability of the wave field for the BS. Figure 6A shows how the monthly SWH varies over the yearly cycle. The SWH is highest in the winter months (Dec–Feb) with a mean of about 1 m throughout this period. In spring, the mean SWH sees a sharp decline to a minimum of approximately 50 cm in May and June. In the second half of the year, the mean SWH gradually increases again. The range of variation is relatively stable, with the years contained within a window of 20 cm (summer) to 40 cm (winter).

The geographic distribution of the mean SWH and wave direction is shown in Figure 6B . It shows a clear separation between the Western (Wb) and Eastern (Eb) sub-basins. The Wb is characterized by N-NE oriented waves with mean SWH values reaching close to 1 m in the majority of the Wb. This wave pattern perfectly matches wind circulation, with northerly winds prevailing in the west and north of the sea (Özsoy et al., 1998; Schrum et al., 2001; Efimov and Anisimov, 2011).

The Eb, on the other hand, shows N-NW oriented waves and a decrease in mean SWH to a minimum of 0.4 m in the easternmost part. The calmest areas of the sea are its southeastern and northwestern parts. The former is not highly affected by the impact of cyclones, whereas the latter is the widest shelf area in the BS, where wave growth is limited by the action of bottom friction (Arkhipkin et al., 2014).

The spatial variations of the mean SWH have been further investigated on a seasonal basis.

In the study, we adopted the conventional methodology in ocean season definition:

Figure 7 , subplots 1, shows the SWH for each season in terms of the mean, maximum, and 5th and 95th percentiles, while the arrows indicate the direction corresponding to each statistic.

The mean and 5th/95th percentiles clearly show the difference between the rougher Wb and calmer Eb. The mean direction follows almost the same pattern throughout all the seasons, similar to the annual average.

The maximum SWH shows an interesting distribution. In winter, it is in line with the other distributions, with the highest values located between the Bosphorus and the Turkish Çatalca peninsula. In spring, however, the maximum SWH occurs in the Crimean–Kerch–Russian area in the calmer Eb. In summer and autumn, the maximum SWH occurs more towards the central Black Sea.

In addition, an increase in the frequency of western, southwestern, and southern waves is evident during spring and summer, arguably due to the influence of the Azores High pressure system (Bondar, 2014).

The main direction of the wave field is in agreement with the literature (Arkhipkin et al., 2014; Divinsky and Kosyan, 2017), showing waves are mainly NE-oriented except for the eastern part of the eastern basin, in which waves are NW-oriented. This pattern is evident for lower waves, 5th percentiles, and the mean wave height, while higher waves (95th percentile and maximum) showed a different pattern: SE waves along the west coast all through the year, and W-SW waves along the east coast.

In Figure 7 , subplots 2, we illustrated the wave direction variability associated with the directions described in Figure 7 , subplots 1. The most uncertain wave direction field is represented by the mean, which has an eastward increase of STD from ~80° to ~120° in all seasons.

All the other statistics manifested a lower variability in direction, in general below 60°. The lower waves (5th percentile) revealed a larger variability with respect to the higher waves (95th percentile and maximum), with a westward increase that spans from ~20° of the Eb to ~50° of the Wb. The higher waves exhibited the largest variability in the northwest of the basin and in the Kerch area, exceeding 70° in some cases. In contrast, the central part of the basin (south of the Crimean Peninsula) and the Wb, which showed the most stable directions, are affected by south-westerly and north-easterly winds, respectively.

The seasonality of the wave field can be further summarized by the seasonal variation index (SV) (Reguero et al., 2013). We excluded MWD from the analysis because the SW index is not suitable for the variable. The index quantifies the range of variation in mean seasonal values in relation to the annual mean, as follows:

where V _Smax represents the maximum value of seasonal means, V _Smin is the minimum, and V _mean represents the total mean of the variable under consideration. Figure 8 shows the index expressed as a percentage. The index allows a sharp identification of the seasonality variation over the basin, showing a general reduction of the SV index from north (~60%variation) to south of the basins (~ 30%variation). The northeast coasts, including the Eastern Crimean Peninsula and the Russian BS coast, exhibit the highest variation, exceeding 80%. This notable peak in SWH variability could be attributed to the extreme wind variability of the area that has been described in a previous study (Akpınar et al., 2016). Notably, this area showed the occurrence of high maximum SWH values during the spring and autumn seasons, but also the very low 5th percentile ( Figure 7 , subplots 1).

In the following section, the inter-annual variability of SWH has been analyzed in terms of the principal mode of variability, both cumulative and at basin scale, and also as geographic distribution of seasonal statistics.

The wave field variability of SWH and wave direction have been computed by PCA. This statistical technique (Zwiers and von Storch, 2004) is extensively applied in climatological analyses. It enables the identification of meaningful components amidst the extensive amount of data, distinguishing them from “noise”, which may be irrelevant in the process of description and understanding the real system (Lionello and Sanna, 2005). PCA is founded on an eigenproblem derived from maximizing the quadratic propriety of the variance. The data transformed through this process delineate the Empirical Orthogonal Functions (EOFs), which represent orthogonal spatial patterns that identify the preferred modes of variability within the system. Principal components (hereinafter, PC) capture the variability of the field and represent the temporal coefficients obtained by projecting the fields onto the EOFs.

In this investigation, the PCA has been applied to SWH, generating a vector with magnitude SWH and direction representing the MWD. Most of the SWH variability is described by the first two EOFs, accounting for 67% and 15% of the total variance ( Figure 9C ).

The firstEOF ( Figure 9A ) represents northeastern waves in the Wb and central BlackSea, as a result of the prevailing northerly winds. Instead, the second EOF ( Figure 9B ) represents the south-southeastern propagating waves in the Eb. The PCA therefore confirms, as far as the wave climate is concerned, the division of the Black Sea into Eastern and Western sub-basins, as we proposed before.

The characterization of the first two EOFs was established through an examination of the composites of SWH ( Figure 10 , subplots 1) and mean sea level pressure (MSLP) ( Figure 10 , subplots 2). In generating each composite, we differentiated between upper and lower phases by considering the average fields of the SWH and MSLP when the associated EOF of the SWH field was in the uppermost/lowermost 10%.

The main mode for the wave climate in the BS is described by Figure 10A1 . This wave field is generated by low pressure located in the Eb along Russian coasts ( Figure 10A2 ) and high pressure in central-western Europe, defining rougher waves in the Wb, mainly N-NE oriented, which exceeded 2 m in height. The lower composite of the first EOF is represented by very smooth wave conditions ( Figure 10B1 ) and low pressure all over the BS domain ( Figure 10B2 ).

The second mode of the BS wave field is shown in Figure 10C1 with NW-W waves exceeding 1.5 m in height in the Eb. This condition is generated by high pressure in Turkey and low pressure in the northeast of the Azov Sea ( Figure 10C2 ). The lower composite of EOF2 shows E-oriented waves, except for the eastern part of the Eb. This wave field provided high waves (exceeding 1.75 m) in the southwest region of the BS, and is defined by low pressure in southern Turkey and high pressure above 47°N.

Therefore, both time and space coefficients have been projected onto cumulative yearly EOFs to highlight the variability of the principal components between years. Figure 11 denoted that, in the last three decades, the first two EOFs had opposite trends, with the weakening of EOF1 and the strengthening of EOF2, even if to a lesser extent: −9% for EOF1 and +4.5% for EOF2. This tendency can be interpreted as the reduction of N-NE waves, mainly driven by winds developed in the MSLP dipole shown in Figure 10A2 , in favor of the frequency intensification of W-oriented waves for Eb ( Figure 10C2 ).

From an MSLP perspective, the changes could be intended as the shifting of higher pressure towards Turkey and the displacement of lower pressure toward the eastern Azov Sea.

The trend analysis through the MK test over the time frame 1988–2021 did not reveal any significant change in SWH climate at basin scale, for all the statistics (5th–95th percentiles, mean, and maximum). There was no statistically significant trend, even when the test was applied at a seasonal scale.

Furthermore, the trend assessment has also been applied in the spatial domain, as depicted in Figure 12 . To enhance the plotting clarity, results of the MK test for SWH are presented in a reduced resolution of approximately 1/3°. Trend values with significance lower than 95% are rejected and masked in the figure.

The seasonal trend investigation ( Figure 12 ) provided a similar spatial pattern between all the statistical descriptors. Two seasons showed a wider spatial covering affected by significant trends for SWH. In winter, a near-majority of the basin (mostly the Wb) is affected by a positive trend, while during autumn, almost all the basin (mostly the Eb) shows a negative trend. The MK test highlighted the absence of trends in spring and a well-defined distinction between the Wb (positive trend) and Eb (negative trend) during summer. The strength of the trend increased as the waves increase: on the average field, the SWH trends varied within a range of ± 0.25 cm/year, while for the highest waves’ statistics (95th percentile and max), the range was ± 0.5 cm/year.

Our comprehensive analysis of the wave inter-annual variability for the BS reveals rougher sea conditions during winter, in contrast with calmer sea conditions during autumn. We hypothesized that the negative trend in autumn may be driven by the increased frequency of lower EOF1. On the other hand, the positive trend during winter in the Eb appears to be dependent on the changes observed in upper EOF2 and MSLP composites, as detailed previously. Concerning the positive trend of the Wb waves, we could not establish a direct association with any of the investigated composites, leading us to conclude that the trend is likely to be related to less recurrent composites.

The last section of the study assessed the relationship between the most important atmospheric teleconnections (TLC) and SWH for the BS domain: East Atlantic Pattern (EA), Scandinavian Pattern (SCA), North Atlantic Oscillation (NAO), and East Atlantic/West Russia Pattern (EA/WR). The indices time series have been provided by https://www.cpc.ncep.noaa.gov/data/teledoc/telecontents.shtml.

One of the most important teleconnection patterns across seasons is the NAO, as identified by Barnston and Livezey (1987). The NAO manifests as a north–south dipole of anomalies, featuring one center situated over Greenland and the other center with an opposite sign, extending across the central latitudes of the North Atlantic. The NAO is characterized by two phases.

The EA pattern emerges as the second significant mode of low-frequency variability over the North Atlantic. It comprises a north–south dipole of anomaly centers spanning from east to west across the North Atlantic. However, the EA pattern is distinguished from the NAO by the lower-latitude center location and its association with the subtropical ridge.

The EA/WR pattern stands out as a key teleconnection pattern influencing Eurasia, characterized by four primary anomaly centers.

The SCA comprises weak centers of opposite signs over western Europe and eastern Russia/western Mongolia (Barnston and Livezey, 1987), governing a primary circulation center over Scandinavia.

The correlation between TLC patterns and SWH fields has been evaluated on a monthly basis, both on the averaged wave field and EOFs. The analysis was limited to the winter season, characterized by active cyclogenesis above the Mediterranean and the Black Sea (Mikhailova and Yurovsky, 2016). During this period, a high-pressure system dominates central Europe, positioned between two pressure centers, over western Russia and the mid-Atlantic.

The investigation revealed that only the EA/WR pattern, for both EOFs and the mean field, has a statistically significant TLC–SWH correlation (p-value<0.05). In detail, from the correlation matrix ( Table 3 ), we observed that the EA/WR pattern showed the largest influence on the wave variability, mainly on EOF1 (0.32), and the pattern is negatively correlated with EOF2 to a lesser extent (−0.19). Considering the mean wave condition of the last three decades at basin scale, the correlation was negative (−0.25). This finding offers new perspectives on the correlation between BS wave and TC indices. It is noteworthy that in the earlier research of Saprykina et al. (2019), the annual mean waves were found to be more affected by the NAO. However, it is important to consider that the two studies investigated different time frames.

An investigation of the spatial distribution of the correlation has shown that the link between TLC patterns and mean SWH is not uniform across the BS basin ( Figure 13 ). Considering the different characteristics of the sub-basins, this is to be expected, as already found and described by Lionello and Galati (2008) for the Mediterranean Sea.

Spatially, most of the domain presented a negative TLC-SWH correlation with an intensification towards the southeast, exceeding −0.5 along the east coasts.

In contrast, the EA/WR pattern has a strong positive link with SWH along the western coasts of Ukraine. This spatial correlation pattern is in agreement with findings from Saprykina et al. (2019). In addition, this investigation revealed no or low correlation for the central part of the Wb along the continental slope.

The correlation analysis indicated the BS wave climate’s clear dependency on the EA/WR pattern, for both its variability (EOFs) and mean. However, the stronger correlation with EOF1 reveals that when the EA/WR pattern is stronger, the seasonal cycle is more intense. The spatial correlation confirmed the distinction between the Wb and Eb wave field that we observed in the previous analyses. During its positive phase, the EA/WR pattern consists of four centers: two positive height anomalies located over north-central Europe and northern China, and two negative height anomalies located over the central North Atlantic and north of the Caspian Sea.

The correlation map accurately matches the dipole pattern located in Europe and Russia, determining a strong positive correlation in the northwestern basin and a strong negative correlation with the southeastern basin.