1 Introduction

The effects of post industrial climate change (CC) on the environment have been investigated by the scientific community since the mid twentieth century. However, the volume of research on the impacts of CC on a wide range of natural physical processes and, in turn, on mitigation measures has rapidly increased in the 2000s. This is the case of ocean/marine processes, for which a large literature is available on the quantification of historical and future impact of CC on, e.g. water temperature (Meredith and King 2005; Abraham et al. 2013; Wijffels et al. 2016), salinity (Helm et al. 2010; Durack et al. 2012), marine biota (Scavia et al. 2002; Munday et al. 2008), ocean circulation (Toggweiler and Russell 2008; Winton et al. 2013), sea level (Milne et al. 2009; Watson et al. 2015; Chen et al. 2017; Dangendorf et al. 2017, among others), and ocean waves climate. The latter aspect has received increased interest thanks to the relevance of coastal erosion and wave energy conversion in recent years. The much improved computing capacity accessible to research groups worldwide, the availability of extensive numerical databases, satellite observations, and wave projections, have all contributed to the development of a large body of work on the analysis of ocean waves trends that can be detected from time series spanning several decades in the past, hereinafter referred to as historical trends. Their analysis is essential to understand the present climate trends.

The topic is of great interest in micro- and meso-tidal environments, such as those found in the Mediterranean Sea (MS), as long-term changes in wave conditions may have strong implications for increased coastal erosion (Satta et al. 2017; Enríquez et al. 2017; Toimil et al. 2020; Simeone et al. 2021) and, in turn, for tourism revenue (Alexandrakis et al. 2015), harbors operation (Casas-Prat and Sierra 2010a; Sánchez-Arcilla et al. 2016) and ships navigation (note that several major ports connect the Mediterranean countries worldwide, making it one of the busiest basins in the world, Mayer et al. 2018), and finally for blue energy production, given that the MS hosts promising hot spots for the conversion of wave energy, see Mattiazzo (2019) and references therein. As such, it is important to provide a broad insight in the wave climate variability in the MS, as well as to identify statistically significant climatic trends.

A large body of research has been devoted to identify historical trends in wave parameters since the 2000s; most of the studies reconstructed multi-decadal time series of ocean waves parameters for the whole MS or one of its sub-basins, from which trends are investigated. The available studies focus on the analysis of trends of the significant wave height \(H_s\), with very few studying other sea states parameters. Even a very quick overview of the literature allows to understand that trends show a rather large spatial variability, with adjacent MS sub-basins sometimes showing opposite behaviour. It is equally evident that the existence of a consensus among these studies is not apparent. Therefore, the aim of the present review is to identify evidence of consistent historical trends of sea states within the MS and its sub-basins. To do so, we analysed the current literature using a top down approach: first we considered articles investigating sea states at whole Earth scale, then at the scale of the whole MS, subsequently we looked into studies of individual or groups of sub-basins; finally, we reviewed articles studying trends at regional or individual locations scale.

This article is organised as follows. Section 2 describes the methodology used for the review. Section 3 describes the trends in \(H_s\) found in the literature and identifies the consensus among studies. Section 4 describes sea state parameters other than \(H_s\). Finally, Sect. 5, draws the conclusions of the article and sets out recommendations for future studies on the topic.

2 Materials and methods

For the present review we considered only peer reviewed articles published starting from 2000; indeed, the time span covered by prior researches would be too short for comparison with up-to-date studies; a list of the articles initially reviewed can be found in the Supplement. Within those we considered only studies that analyse multi-decadal trends in sea states, which excludes, for example, analyses of long term storms characteristics (e.g. Besio et al. 2017; Amarouche and Akpınar 2021). Within the reviewed literature the domain of analysis varies from the whole Earth, to regional studies of stretches of coast of the order of \(10^2\) km. We refer to global scale of analysis to indicate studies that examined the MS as part of a worldwide dataset. Similarly, regional scale is used for the analysis of the MS only or, at least, one of the sub-basins into which it is traditionally divided. Finally, local scale refers to studies of single locations or coastal stretches. Note that no global scale study was found to discuss sub-basins, due to the coarser resolution used with respect to the other two scales of analysis. The mesh resolution for the numerical simulations used, however, does not consistently increase for local scale studies with respect to regional ones. Studies at regional scale often discuss trends at sub-basin scale, but these are analysed in this review separately from studies in which the focus is purely local.

Wave data series employed in the articles reviewed were retrieved from different sources, such as hindcast and re-analysis with numerical models, satellite altimeters, buoys, pressure transducers, and ship observations (from Voluntary Observing Ships, VOS). Most of the articles reviewed used modelled data (either hindcast or reanalysis; see Fig. 1), as these provided the longest continuous time-series, allowing for sounder trend estimates. A note of caution should be provided in considering trends identified in the literature from studies using multiple data sources or numerical results from different products, or reference periods. For example data availability in time series obtained from satellite altimeters, i.e. the density of satellite tracks, was found to affect high percentile trends (Young and Ribal 2022), together with data calibration, i.e. on whether this is performed and what is the benchmark considered. The importance of the specific satellite wave products analysed was also highlighted by Timmermans et al. (2020), who pointed out discrepancies in trend estimates which depend on the data employed. Significant divergences in trend estimates can also be found when comparing hindcast and reanalysis products. As for the latter, modelled wave climate can be greatly affected by data assimilation (Meucci et al. 2020; Erikson et al. 2022). This occurs because there was a significant surge in data assimilated by the models during the early 1990s when satellite assimilation began (Timmermans et al. 2020; Erikson et al. 2022). Furthermore, the trends in model reanalysis are influenced by the growing number of satellite observations assimilated over the years (Sharmar et al. 2021). A further influence on the trends estimate in modelled data using VOS assimilation, may be the lack of standards for measuring surface wind speed in VOS in part of the twentieth century. Even a single model, when initialized with different initial conditions, can yield opposite trends worldwide (Casas-Prat et al. 2022). These factors are crucial when assessing conflicting results, such as opposing trends observed in numerical studies.

Fig. 1
figure 1

Data sources used for the analysis of wave parameters in the literature reviewed. Note that the number of sources exceeds the number of articles reviewed because multiple sources are used by some articles. For the sake of clarity, both reanalysis and hindcast are referred as “simulations” (although they differ as the former use ocean wave data assimilation while the latter do not). “Point” denotes point measurements using buoys (Timmermans et al. 2020) and pressure transducers (Pomaro et al. 2017)

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Trends were mainly detected using the Mann-Kendall test (Mann 1945; Kendall 1948, hereinafter shortened as MK) and the corresponding seasonal test for monthly averaged series (Hirsch et al. 1982), and were quantified either through linear fit (LF), or the Theil–Sen estimator (Theil 1992, TS), which is based on the Kendall’s rank estimator and it is therefore often used along with MK (the two parameters are in fact well correlated, as shown e.g. in De Leo et al. 2020). Indeed, TS and MK are the most popular methods used to quantify trends and assess their significance, respectively (see Fig. 2). The TS slope allows to filter possible outliers and it is therefore more robust than simple LF, although the two metrics were proved to yield comparable results (Timmermans et al. 2020; Lin and Oey 2019). A group of works assessed trend significance through the Student’s t-test (Gulev and Grigorieva 2004; Martucci et al. 2010; Sharmar et al. 2021; Amarouche et al. 2022); the Wilcoxon test, and the test of Hayashi (1982) (Gulev and Grigorieva 2004); an F-test (Lionello and Sanna 2005); the time-varying location of a non-stationary Generalised Extreme Value Distribution (De Leo et al. 2021a) denoted with \(\mu _t\); methods based on bootstrap (Casas-Prat and Sierra 2010b, a, 2012; Timmermans et al. 2020); the analysis of LF confidence intervals (CI) (Young et al. 2012); the Innovative Trend Analysis (or ITA; Şen 2012), to be coupled with other trend metrics (Caloiero et al. 2019; De Leo et al. 2020; Lo Feudo et al. 2022). The latter test was proved to be affected by few shortcomings (Serinaldi et al. 2020), thus it should be used with caution.

Fig. 2
figure 2

Number of occurrences of tests employed for trend detection and quantification in the literature reviewed. The group labeled with “other” embeds the tests used only in a single article (Wilcoxon and Hayashi tests, \(\mu _t\), F-test, either LF or TS with no significance measures). Note that the number of tests exceeds the number of articles reviewed because multiple tests are used in some articles

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In order to assess the results on changes in wave climate for each area of the MS, we only considered studies presenting analysis of \(H_s\). This restricted the review to 26 articles, which are listed in Tables 1, 2, and 3 (global, regional, local analysis respectively); these report the products employed (note that numerical models are here collectively referred as simulations), time periods covered by the data, and analysed wave statistics.

To facilitate the comprehension of the results, the MS is here grouped in the sub-basins shown in Fig. 3, namely: Alboran Sea (A\(_l\)S), Balearic Sea (BS), South-West MS (SW-MS), Gulf of Lion (GL), Ligurian Sea (L\(_i\)S), Tyrrhenian Sea (T\(_y\)S), Straight of Sicily (SS), Gulf of Sirte (GS), Ionian Sea (IS), Aegean Sea (A\(_e\)S), Adriatic Sea (A\(_d\)S), and Levantine Sea (L\(_e\)S). Note that, for the sake of simplicity, some of the basins were named after well known features they include, although they span wider areas (for example, the Gulf of Sirte extends to Egypt beyond the Lybian coastline).

Table 1 List of articles reviewed
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Table 2 As in Table 1 for regional scale analysis
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Table 3 As in Table 1 for local scale analysis
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Fig. 3
figure 3

Basins used to group trend estimates in the MS: Alboran Sea (A\(_\text {l}\)S in the figure); Balearic Sea (BS); South-West MS (SW-MS); Gulf of Lion (GL); Ligurian Sea (L\(_\text {i}\)S); Tyrrhenian Sea (T\(_\text {y}\)S); Straight of Sicily (SS); Gulf of Sirte (GS); Ionian Sea (IS); Adriatic Sea (A\(_\text {d}\)S); Aegean Sea (A\(_\text {e}\)S); Levantine Sea (L\(_\text {e}\)S)

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We counted the number of articles detecting either positive or negative trends in each of the sub-basins. A preliminary analysis of the literature showed that, within some sub-basins, trends with opposite signs in different areas were identified; therefore, we split the analysis between upward and downward trends, extracting the respective ranges of variability and checking for the presence of significant ones. However, inferring the exact trends magnitude from the spatial maps provided in the literature is not trivial, especially when continuous color scales are used to show results. Besides, in case of blank areas, it is sometimes difficult to understand whether an article detected negligible trends or the area was not covered by data (especially at low spatial resolution; see for example the trends in the Adriatic Sea resulting from Young and Ribal, 2019; Cao et al., 2021). For this reason, in this review more attention is paid to trends sign and significance rather than the exact annual rates of change.

To summarise \(H_s\) trends for each sub-basin, we pooled together all the findings on mean, median (p50), and modal \(H_s\), deemed representative of mean climate conditions. On the other hand, results for percentiles higher than 90th and annual maxima \(H_s\) were considered jointly and referred to as extreme sea states (see Fig. 4; a similar approach is used by Ratsimandresy et al. 2008). Note that the ith percentile is henceforth shortened to pi (e.g. the 90th percentile is indicated as p90). We retained trends arising from both annual and monthly series; although the latter may be affected by seasonal periodicity, this is usually filtered out using appropriate metrics, such as seasonal-MK; in this respect, see e.g. Young and Ribal (2019), who claimed that trends of monthly series can be extended to annual statistics. As for trends on seasonal subsets, we only retained those computed for extreme sea states over winter months, as these are representative of yearly extremes in the MS. By contrast, trends on seasonal mean such as in Timmermans et al. (2020) cannot be directly compared to annual statistics. In case of studies presenting analysis at both yearly and seasonal results (Zacharioudaki et al. 2015; Caloiero et al. 2022), we only considered the former. As for the significance of trends, we consider that a significant trend is present in a sub-basin if this is detected in any area regardless of its extension. While this approach may overestimate the number of articles finding trends at given basins, it allows for a quick assessment and to refine the analysis in hot-spots if needed.

Fig. 4
figure 4

Number of occurrences of \(H_s\) statistics employed for trend detection and quantification in the literature reviewed. Black, grey, and white bins denote annual, seasonal, and monthly statistics, respectively. \(H^{100}\) indicates 100 years return period wave (Young et al. 2012)

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3 Significant wave height trends

3.1 Global analysis

Studies examining global-scale trends employed VOS (Volunteer Observing Ships), satellite altimetry data, and numerical results with resolutions ranging from \(0.25^{\circ }\) to \(4^{\circ }\) in both latitude and longitude, which corresponds to approximately 25 km to 400 km at the MS latitudes (see Table 1). Inevitably, this has an impact on the resolution of the results for the sub-basins. Besides, time-series related to nearby locations are often pooled together, potentially adding further uncertainty to the trend estimates.

For mean wave climates, widespread significant and positive trends over the whole MS were detected by Lin and Oey (2019) (with the exception of the Straight of Sicily), and Meucci et al. (2020) when using reanalysis products (while they found no trends when relying on a model-only integration). Also Gulev and Grigorieva (2004) found positive and significant trends based on VOS; however, their results may be biased since ships tend to avoid stormy conditions. By contrast, Young et al. (2011) mostly detected significant and negative trends over vast areas in the central MS, while no significant trends could be later identified by Young and Ribal (2019). Their results greatly diverge for mode and mean \(H_s\) series, suggesting that changes have occurred in the shapes of the wave height pdf’s over the 33-year measurement period. No significant trends were neither found by Casas-Prat et al. (2022) nor by Cao et al. (2021); as for the latter, they only spotted positive and significant trends during the so called slow-down period (1999–2013) especially in the Ionian Sea. Such discrepancies call into question the reliability of trends found using short time series. In this respect, Sharmar et al. (2021) showed how to rely on different periods can result in opposite trends within the Northeast Pacific Ocean, Northeast Atlantic Ocean, and South Indian Ocean; they also found diverging results when comparing trends based on ERA products (which incorporates both wind speed and wave height measurements) and Climate Forecast System Reanalysis, CFSR (which only only assimilate wind speed data). On the contrary, a high consensus in seasonal p50 and p90 trends estimates was pointed out by Erikson et al. (2022) based on a 7-members ensemble of global wave products by not considering CFSR data. The season analysed plays also a crucial role in trends assessment: for example, all data used in Timmermans et al. (2020) yield significant upward trends in the Gulf of Lion for January, February, and March, but none leads to significant-positive trends for June, August, and September. However, note that seasons at the MS latitudes are more commonly grouped in December, January, and February (winter)–March, April, and May (spring)–June, July, and August (summer)–September, October, and November (fall; e.g., Erikson et al. 2022) and an objective definition of season (e.g. Kotsias et al. 2021) is not always used in the reviewed literature.

In case of extreme wave climates, no significant trend patters were highlighted by Young et al. (2011) and Sharmar et al. (2021), while Casas-Prat et al. (2022) found widespread and positive (negative) trends in the eastern (western) MS, although not significant. By contrast, positive and significant trends characterize the western Mediterranean in Young and Ribal (2019). No significant trends can be appreciated in the MS for high return period waves: Young et al. (2012) assessed trends for 100 years \(H_s\) computed starting from 4-year long time slices, an interval too short to obtain reliable estimates; in fact, the computed variability due to trends is comparable to the confidence intervals of the return levels. Also Takbash and Young (2020) investigated trends in the 100 years \(H_s\), but did not include the MS in their analysis.

3.2 Mediterranean basin analysis

In case of articles investigating trends at the regional and sub-basin scales, more detailed analysis can be often drawn thanks to higher spatial resolutions, which is found in the literature to range between \(0.05^{\circ }\) and \(0.25^{\circ }\) in studies using numerical hindcast. High-resolution numerical weather hindcasts can indeed reproduce small-scale structures even if these are not fully captured by large-scale forcing (Skamarock 2004), hence wave hindcast benefit from increased resolution in wind forcing. However, uncertainties may arise from the model physical calibration parameters, from boundary conditions in case sub-basins are numerically simulated, and/or propagate across different scales (Wilby and Dessai 2010) throughout the downscaling process (Shepherd et al. 2018). For example, Caloiero et al. (2019) downscaled hindcast data from deep waters to several coastal location around Calabria (South of Italy), and found trends not fully consistent to their offshore counterparts. As a matter of fact, wave propagation can be another step affecting trend estimates, prompting the need to carefully calibrate wave models for coastal environments (see in this respect De Leo et al. 2022). The above considerations can partly explain the divergences in trends results identified by studies using different model setups/products, as shown below.

For the mean wave climate, Caloiero et al. (2022) and Amarouche et al. (2022) highlighted positive and significant trends distributed over the whole MS and the western MS, respectively; on the contrary, Musić and Nicković (2008) mainly found negative trends in the western MS. Similar findings were presenred by Zacharioudaki et al. (2015), De Leo et al. (2020), Barbariol et al. (2021), and Elshinnawy and Antolínez (2023), who highlighted negative and significant trends clustered in the Levantine Basin, with Elshinnawy and Antolínez (2023)showing positive and significant trends in the Alboran Sea only. Sub-basins and single locations within the MS were analysed in few works. Negative and significant trends were computed in the Adriatic, the Ionian, and the Tyrrhenian Seas by Martucci et al. (2010), while Pomaro et al. (2017) found positive trends in the North Adriatic Sea. Finally, Lo Feudo et al. (2022) analysed trends in mean wave climate on annual, seasonal, and monthly time scales at a single site in front of Calabria coastline (South Tyrrhenian Sea) and could not find significant ones for \(H_s\).

For the extreme sea states, results from De Leo et al. (2020), Amarouche et al. (2022) diverge from those by Caloiero et al. (2022), in particular for the annual maxima \(H_s\) south of the Gulf of Lion. Both De Leo et al. (2020) and Amarouche et al. (2022) found negative trends there, contrarily to Caloiero et al. (2020), whose results are consistent with those by Elshinnawy and Antolínez (2023). The aforementioned differences can be also explained by the different confidence levels used to detect trends through the MK, i.e., 5% (De Leo et al. 2020; Amarouche et al. 2022) and 10% (Caloiero et al. 2022; Elshinnawy and Antolínez 2023); and different statistics to characterise extreme and mean conditions (p99.5 and median rather than AM and mean in Elshinnawy and Antolínez 2023). Results by De Leo et al. (2020) were further confirmed by De Leo et al. (2021a), who assessed the rate of change of the location parameter (\(\mu _t\)) of non-stationary Generalised Extreme Value distribution for annual maxima \(H_s\). Interestingly, all the above mentioned researches found negative and significant trends in the Southern Thyrrenian Sea. Zacharioudaki et al. (2015) highlighted widespread positive and significant trends west of the Crete Island (Greece) for annual p99 \(H_s\) series when taking 1960–1981 as a reference interval. The same analysis led to opposite trends for the 1981–2001 period, showing consistency issues discussed in Sect. 2; even more so, since trends showed a marked seasonal variability. Similar findings were pointed out by Barbariol et al. (2021); Amarouche et al. (2022); Caloiero et al. (2022); Elshinnawy and Antolínez (2023) who remarked that, in case of seasonal analysis, trends can change dramatically depending on the months subset considered; in particular, trends computed for June–September subsets are milder, because of the low magnitude of sea states compared to extreme data, such as AM, that usually occur during winter time. Additional analysis were carried out by Caloiero et al. (2020) and Caloiero and Aristodemo (2021) based on the ERA-Iterim dataset (Dee et al. 2011); however, further on in the article we only consider Caloiero et al. (2022), as this embeds the results of the previous works (in the latter work authors have extended the analysed area adopting the same data and the same methodology).

3.3 Consensus

Using the distinction between mean climate conditions and extreme sea states and the methodology explained in Sect. 2 we counted the negative and positive trends found for each sub-basin of the MS and distinguished between significant and not significant ones. Summary of the results are shown in Fig. 5 (mean wave climate) and Fig. 6 (extreme sea states). The number of researches either detecting trends (significant and not significant) or not finding any are normalised over the total number of research per each basin (such ratio is referred to as \(\chi\) in the figures, with subscript \({-}\) and + to indicate negative and positive trends respectively). Note that negative and positive trends can be detected in different parts of the same sub-basin, hence \(\chi ^++\chi ^-\) can be larger than 1. In the figure NA indicates either that the significance was not assessed in the study considered or that no trends were identified.

Fig. 5
figure 5

Summary of the research investigating trends for mean wave climate. Left side: positive trends; right side: negative trends. The number of researches either detecting trends (significant and not significant) or not finding any are normalised over the total number of research per each basin (such ratio is referred to as \(\chi\) in the figures)

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Fig. 6
figure 6

Same as Fig. 5 for extreme sea states

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Overall, for mean climate trends, works finding mean negative trends represent the majority for most basins (right side of Fig. 5). However, when significant trends only are considered, positive and negative trends are almost as frequent. Significant trends are detected predominantly in the the western MS and in the Gulf of Sirte. In particular in the Gulf of Lion, and the South-West MS (left side of Fig. 5) positive significant trends are more abundant than non significant or unclassified trends. This is never the case for negative trends. In case of extreme sea states trends, there are many basins where, although some trends could be identified, these were mostly found to be unclassified or not statistically significant; such consideration holds for 10 out of 12 basins for positive trends, and for all basins in case of negative trends.

Looking at the significant trends, the Gulf of Lion is the basin most affected by upward significant trends, that are mostly located in the west part of this sub-basin. The Tyrrhenian Sea is also interested by positive and significant extreme sea states trends. This basin is also the one showing the largest amount of researches finding negative and significant trends. These trends coexist in the same sub-basin and show a clear north/south split, with negative trends located in the southern sub-basin (off the Calabria coast, Italy) and the positive in the northern part (towards the Ligurian Sea), respectively, (De Leo et al. 2020; De Leo et al. 2021a; Caloiero et al. 2022; Amarouche et al. 2022), therefore they should be further analysed.

The consensus on the relation between trends in sea states and long-term changes in weather patterns is also not general. Correlations between winter averaged \(H_s\) series and the North Atlantic Oscillation (NAO) and Scandinavian index have been investigated (Lionello and Sanna 2005; Barbariol et al. 2021), as well as links between wave climate variability and the Mediterranean Oscillation Index and the East Atlantic pattern (Elshinnawy and Antolínez 2023; Izaguirre et al. 2010). However, inter-annual variability in wave climate can only partly be explained by teleconnections (Barbariol et al. 2021), since wave regimes are more closely related to local centers of action (Lionello and Sanna 2005) and local generated wind (Lin and Oey 2019; Cao et al. 2021), although this does not imply that wave trends mirror trends in wind climate (Alves 2006).

4 Other sea state parameters

For most coastal and off-shore projects and operations, \(H_s\) is the most relevant parameter. Hence, the vast majority of articles reviewed attempted to assess climatic trends by analysing time series of \(H_s\) data. However, other parameters can also play a crucial note; in particular, changes in waves direction of propagation \(\theta\) can directly affect shoreline dynamics (Zacharioudaki and Reeve 2011; Casas-Prat and Sierra 2012; Chataigner et al. 2022) and harbour agitation (Casas-Prat and Sierra 2012; Sierra et al. 2017). Trends in \(\theta\) need to be assessed independently, as this cannot be inferred from \(H_s\), unlike the wave period, for which simplified parametric formulae can be employed, at least in case of extreme waves when the two parameters are almost linearly related (see e.g., Goda 2003; Callaghan et al. 2008). Moreover, estimation of trends in wave direction is a challenging task due to the intrinsic nature of the data to analyse: peak direction \(\theta _p\), for example, is a non-continuous quantity that depends strongly on the spectral grid resolution and hence could present different behaviour depending on the number of bins employed for partitioning the spectrum; mean direction \(\theta _m\), on the other hand, may not represent the real direction of propagation of wave storms, especially in an enclosed sea such as the MS, where swell conditions are rare, while ocean waves and multiple wave systems occur frequently. For these reasons, to date, little research has been carried out on trends in time-series of \(\theta\) in the MS. Time-series of storms belonging to different directional sectors can be characterised by opposite trends (Casas-Prat and Sierra 2010b), shedding light on a crucial aspect: CC may differently affect storms that propagate from different directions (results were further confirmed in Casas-Prat and Sierra 2010a, 2012). Sierra et al. (2017) and De Leo et al. (2021b) assessed trends in future wave projections and could not find relevant changes with respect to present conditions, while Erikson et al. (2022) highlighted mild counter clockwise trends in annual series of mean \(\theta _m\) in the Levantine Basin. Trends in wave period are even less studied. To the best of our knowledge, wave periods at global scale were analysed only by Gao et al. (2021) and Erikson et al. (2022). However, previous works estimated trends in wave storminess, therefore coupling information about \(H_s\) with storms frequency and duration, which could dramatically affect wave climate trends (Casas-Prat and Sierra 2010b; Lira-Loarca et al. 2021b). In this respect, the analysis of trends in series of Total Storm Wave Energy (Arena et al. 2015) and Storm Power Index (Dolan and Davis 1992) carried out by Amarouche and Akpınar (2021) found patterns similar to \(H_s\) trends in the Tyrrhenian Sea; other hot spots were spotted in the Gulf of Lion (towards the Balearic Sea) and in the Alboran Sea. Such patterns were altered when computing trends on a decadal base (Amarouche et al. 2022). Finally, no significant trends in the yearly number of rough sea states were reported by Erikson et al. (2022).

5 Conclusions

This review analysed the results of peer reviewed articles researching historical ocean waves trends in the Mediterranean Sea (MS). Most of the studies focused on the significant wave height \(H_s\) trends, while other sea state parameters, notably wave direction and period appear to be under-studied in this context. Previous research indicated limited consensus across all levels of \(H_s\) analysed in the MS, neither for mean (Fig. 5) nor for extreme (Fig. 6) \(H_s\). Negative mean wave climate trends are more frequently detected across the MS than positive ones. However, the western MS shows notable, statistically significant, positive trends. Similarly, for extreme sea state positive trends are detected in the western MS, in particular in the Gulf of Lion and the Tyrrhenian Sea, with complex spatial distribution. The western MS is, therefore, the only sub-basin in which positive historical trends are found for both mean wave climate and extreme values of \(H_s\) by a number of studies.

Some considerations should be provided on the links between historical trends and future projected trends, which have not been the focus of this review. However, given the importance of the use of projections in studies aimed at assessing climate scenarios, it is worth pointing out that, for the MS, historical trends and future projected trends diverge. Projections are obtained from future emissions scenarios, which differ from the past, therefore this difference is not surprising. The works by Sierra et al. (2017) off the island of Menorca, Benetazzo et al. (2012); Ruol et al. (2022) in the Adriatic Sea, De Leo et al. (2021b); Lira-Loarca et al. (2021a, 2021b); Simonetti and Cappietti (2023) and Morim et al. (2021) at regional and global scales, respectively, all indicate a decrease in the magnitude of future wave climate within the MS.

The lack of consensus found in this review may be due to the sources of uncertainty that have been proven to affect trend estimates, such as data source (Timmermans et al. 2020), statistics employed to characterise mean or extreme conditions (Young and Ribal 2019), length of the time period used for the analysis (Zacharioudaki et al. 2015; Cao et al. 2021; Sharmar et al. 2021), and thresholds used to prove trends statistical significance (De Leo et al. 2020; Caloiero et al. 2022). Also, in addition to the effect of the different sources of data, within the same source, the varying spatial and time resolution used in various studies may contribute to the lack of a wider consensus on regional trends. This aspect has not been analysed in detail yet. Similarly, for studies using numerical models, the effect of increase of observations in assimilation, known to introduce spurious trends (Wohland et al. 2019; Meucci et al. 2020), is not always considered in the studies in which reanalysis is used. The availability of increasingly longer time series, such as the ERA5 database, may drive studies on the reconstruction of historical trends spanning longer periods, therefore the quantification of the effect of different data assimilated on trends should be considered as a priority.

Based on the above-mentioned aspects, it is clear that the current state of the art on the knowledge of historical trends in the MS, while providing useful insights, needs to improve the reliability of the results by an improved quantification of the uncertainty due to the data and models used. Additionally, also methods used to detect trends and their statistical significance should be improved, above all when multiple studies are compared. While linear trends represent a helpful and straightforward information, the variability of the modelling hypotheses and observations used can generate large variability among studies (Morim et al. 2019), as also observed in the studies reviewed here. Future research should mitigate this by, for example, using an approach similar to that used for projections, where local results are corrected for bias and averaged on individual grid points before determining a trend, (see Lira-Loarca et al. 2023, and references therein), although this does not ensure to span the total uncertainty (Shepherd et al. 2018). Linear trends estimates based on time series at one location themselves should be thoroughly validated by e.g., using multiple tests and possibly analysing the sensitivity to the reference time period and data employed.

A further area in which research is needed is the establishment of links between sea state trends and weather patterns, in which, as discussed in Sect. 3.3, a wide consensus is not present. In this aspect it is needed to understand the role of indexes interpreting weather processes at scales larger than the MS, and changes in local ones. However, this analysis is complicated by the lack of consensus on the significant trends. As noted throughout this review, available studies mainly focus on \(H_s\) trends, with other sea states parameter being understudied. In addition the spatial coherence of the trends within sub-basins has not yet been assessed. For the former aspect, an alternative to analyse spectral periods, is potentially the analysis of full spectra, which has been shown to allow for more robust analysis than the integrated wave parameters, see Lira-Loarca and Besio (2022). For the latter aspect, it is crucial to understand the actual spatial coherence of trends, as done in the field of sea level trends analysis (Calafat et al. 2022).

6 Supplementary information

The list of articles reviewed with their bibliographical information and type of analysis (global, regional, or local) is provided as supplementary spreadsheet file.