# Wind-wave climate changes and their impacts

Mercè Casas-Prat, Mark A. Hemer, Guillaume Dodet, Joao Morim, Xiaolan

L. Wang, Nobuhito Mori, Ian Young, Li Erikson, Bahareh Kamranzad,

Prashant Kumar, et al.

► To cite this version:

Mercè Casas-Prat, Mark A. Hemer, Guillaume Dodet, Joao Morim, Xiaolan L. Wang, et al., Wind-wave climate changes and their impacts. Nature Reviews Earth & Environment, 2024, 5, pp.23-42. 10.1038/s43017-023-00502-0. hal-04573204

HAL Id: hal-04573204

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Submitted on 3 Oct 2025

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# Wind-wave climate changes and their impacts

Casas-Prat Mercè <fnref n="1" />,*, Hemer Mark A. <fnref n="2" />, Dodet Guillaume <fnref n="3" />, Morim Joao <fnref n="4" />, Wang Xiaolan L. <fnref n="1" />,
Mori Nobuhito <fnref n="5" />, Young Ian <fnref n="6" />, Erikson Li <fnref n="7" />, Kamranzad Bahareh <fnref n="8" />, Kumar Prashant <fnref n="9" />,
Menéndez Melisa <fnref n="10" />, Feng Yang <fnref n="1" />

## Abstract :

Wind-waves have an important role in Earth system dynamics through air-sea interactions and are key drivers of coastal and offshore hydro-morphodynamics that affect communities, ecosystems, infrastructure and operations. In this Review, we outline historical and projected changes in the wind-wave climate over the world's oceans, and their impacts. Historical trend analysis is challenging owing to the presence of temporal inhomogeneities from increased numbers and types of assimilated data. Nevertheless, there is general agreement over a consistent historical increase in mean wave height of 1–3 cm yr⁻<fnref n="1" /> in the Southern and Arctic Oceans, with extremes increasing by >10 cm yr⁻<fnref n="1" /> for the latter. By 2100, mean wave height is projected to rise by 5–10% in the Southern Ocean and eastern tropical South Pacific, and by >100% in the Arctic Ocean. By contrast, reductions in mean wave height up to 10% are expected in the North Atlantic and North Pacific, with regional variability and uncertainty for changes in extremes. Differences between 1.5 °C and warmer worlds reveal the potential benefit of limiting anthropogenic warming. Resolving global-scale climate change impacts on coastal processes and atmospheric-ocean-wave interactions requires a step-up in observational and modeling capabilities, including enhanced spatiotemporal resolution and coverage of observations, more homogeneous data products, multidisciplinary model improvement, and better sampling of uncertainty with larger ensembles.

**Keywords** : Climate change, Physical oceanography, Projection and prediction

<footnote n="1">¹ Environment and Climate Change Canada, Climate Research Division, Science and Technology Branch, Toronto, Ontario, Canada</footnote>

<footnote n="2">² CSIRO Environment, Hobart, Tasmania, Australia</footnote>

<footnote n="3">³ Univ. Brest, CNRS, IFREMER, IRD, Laboratoire d'Océanographie Physique et Spatiale, Brest, France</footnote>

<footnote n="4">⁴ Coastal Risks and Engineering Lab, University of Central Florida, Orlando, FL, USA</footnote>

<footnote n="5">⁵ Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan</footnote>

<footnote n="6">⁶ Department of Infrastructure Engineering, University of Melbourne, Parkville, Victoria, Australia</footnote>

<footnote n="7">⁷ US Geological Survey, Pacific Coastal and Marine Science Center, Santa Cruz, CA, USA</footnote>

<footnote n="8">⁸ Department of Civil and Environmental Engineering, University of Strathclyde, Glasgow, UK</footnote>

<footnote n="9">⁹ Department of Applied Sciences, National Institute of Technology, Delhi, India</footnote>

<footnote n="10">¹⁰ Environmental Hydraulics Institute (IHCantabria), Universidad de Cantabria, Santander, Spain</footnote>

<footnote>* Corresponding author : Mercé Casas-Prat, email address : merce.casasprat@ec.gc.ca</footnote>
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# Introduction

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Differential heating of the earth's surface drives winds across the ocean surface, that in-turn transfer some of their energy to the water in the form of surface ocean wind-waves¹, also called surface gravity waves². At any point, the wind-wave field is a spectrum of superimposed waves generated by winds from several distributed weather systems that have met at that point in space and time, including the locally generated wind sea states and the long-travelled swells². The combination of these wind-wave systems define altogether the sea state, which is considered an Essential Ocean Variable (EOV) and an Essential Climatic Variable (ECV) by the Global Ocean Observing System (GOOS) and the World Meteorological Organization (WMO), respectively. It is well established that wind-waves respond to changes in atmospheric circulation (wind speed, direction, and duration), and changes in fetch (for example, with changes in sea-ice distribution)³. Wind-waves can also be
modulated by intense currents⁴ and strong nearshore bathymetric gradients⁵. Wind-waves are dominant contributors to coastal hydro-morphodynamics⁶,⁷ and have an important role in navigation and offshore industry⁸. Also, they are a potential source of renewable marine energy⁹⁻¹¹, which could contribute to the development of sustainable blue economy¹²,¹³.

Natural and anthropogenically-forced climate variability drive changes in wind-waves, that can be experienced as changes in wave height, period (or wave-length), energy (or power), and/or the direction in which they travel¹⁴. The resultant changes in the wind-wave climatology have important consequences, with influence on marine and coastal engineering, industrial operations, and environmental management. For example, future changes in wind-waves might exacerbate coastal erosion¹⁵⁻¹⁸, and flooding¹⁵,¹⁹,²⁰, affect the stability of (largerly expanding²¹) marine-built infrastructure²², threaten the safety of offshore operations²³, and disrupt coastal ecosystems²⁴. Furthermore, changes in wind-wave characteristics may drive potential feedback to the climate system through modulation of fluxes across the air-sea interface, wave-ice interactions, or other processes²⁵,²⁶.

Following the fourth assessment report (AR4) of the United Nations (UN) Intergovernmental Panel for Climate Change (IPCC)²⁷, which highlighted low confidence in future ocean wave climate projections, interest in historical and projected changes in wind-wave climate has received much attention – at least in part driven by the interests of the WMO supported Coordinated Ocean Wave Climate Project (COWCLIP)²⁸. Implications of historical and future wind-wave climate change extend from global down to local scales, and there is now a large body of literature that span this space and time-scales. Coordinated activities assessing historical change at the global scale (for example, through the European Space Agency Sea State Climate Change Initiative²⁹, the Copernicus Marine Service³⁰, global wave hindcasts/reanalysis³¹, and other global data products³²) and community ensembles of global wave climate projections³³⁻³⁸ have improved the perspective of wave climate change at the global scale. Meanwhile, there have been many studies investigating wave climate change at local to regional scales with existing local and regional studies unevenly spanning the world oceans/seas³⁴. This increase in the body of literature is reflected in the IPCC's AR6³⁹, which indicates medium confidence for the projections of changes in mean wave climate but confidence in extreme wave conditions remains low.

In this review, we build a global perspective of historical and future projected wind-wave climate change, piecing together evidence from local, regional, and global studies. We begin by presenting a general overview of the state-of-the-art methods and datasets, while identifying key challenges. Next, we synthesize the main features of the historical and future wind-waves by ocean basin, including their relations with atmospheric teleconnection patterns. We also provide illustrative examples of implications of wind-wave changes. We end with a summary and discussion of perspectives for future research.

## Data, methods and key challenges

With existing research now expanding several decades, we possess a solid understanding of the main features of the historical wind-wave climate and potential future changes in a warmer world. However, there are still significant uncertainties related to our observational and modelling capabilities despite continuous improvements. In this section, we present an overview of the main available datasets and methods to study historical and future wave conditions, as well as the associated limitations and challenges.

### Historical wave climate

The wind-wave climatology has received particular attention since the second half of the 20th century. The North Atlantic was a first focus for wind-wave climate research⁴⁰ as military operations, oil exploration, and shipping activities between Europe and the US required a detailed understanding of sea state variability. Increasingly, deployment of in-situ wave observations (wave buoys), coordination of voluntary observing ship (VOS) records of sea state⁴¹, the availability of regional and global scale wind-wave hindcasts and reanalyses, and satellite observations (primarily altimeter, with increasing exploitation of other sensors such as Synthetic Aperture Radars, SAR, and wave spectrometer⁴²,⁴³), have provided longer and more suitable datasets for deriving wind-wave climatology and its variability over the global oceans over at least a few decades²⁹,³²,⁴⁴, and are critical supplements to study the regional wave climate.

Despite the substantial increase in wave observations over the last years, their temporal and spatial coverage remains heterogeneous, and long wave records are scarce. For instance, moored buoys are mostly located in the North Hemisphere and just a small fraction of them exceeds 40 years of data (Fig. 1(a)). Additionally, observations are affected by temporal inhomogeneities⁴⁵ due to changes in network characteristics over time (for example, device modernization, relocation, increase in sampling frequency) and quality control and postprocessing procedures. In general, temporal inhomogeneities can be defined as temporal variations or discontinuities in observed records (or climate products that assimilate observations) that result from non-climatic factors such as changes in the way the measurements were performed. With now more than 30 years of data (Fig. 1(b)), satellite remote sensing offers valuable information. However, differences in multi-mission calibration procedures can lead to differences in resulting climatological values, and, particularly, trends⁴⁴,⁴⁶ (Figs. 2(a) and S1). Moreover, its sparse sampling pattern leads to undersampling errors that particularly affect the extremes of earlier periods with a lower amount of in-orbit altimeters⁴⁷. For example, only one altimeter mission (GEOSTAT) was in orbit over 1985-1990³² (with
the next mission starting late 1991), whereas 8 altimeter missions were in orbit in 2020⁴⁸. One promising way to supplement altimetry undersampling could stem from the combined use of SAR missions. Despite a lower SAR wave mode acquisition rate (~100km) compared to the 1Hz altimeter data (~7km), the wave spectral information derived from SAR images can be used to propagate swell properties along great circles from their source regions to the coastline⁴⁹, and therefore increase the wave population density.

To overcome the limitations associated with observations, wave hindcasts and reanalyses³⁰,³¹ are often used as observation proxies (wave hindcasts do not assimilate wave observations but both wave reanalysis and hindcast products indirectly account for assimilated atmospheric observations). They are invaluable tools that have helped advance understanding of the historical wave climate at global and regional scales. Wave hindcasts/reanalysis and satellite data have also been used to demonstrate the relation between global wave characteristics and leading teleconnection patterns that are known to be closely associated with general climate variability over multiple time-scales⁵⁰⁻⁵². Existing literature has largely focused on integrated wave parameters such as the significant wave height ($H_s$), the mean wave period ($T_m$) and the mean wave direction ($\theta_m$) (see Box 1), with a limited amount of wave products developed for the full wave spectrum⁵³.

Existing research provides no clear evidence about what wave product can be used as a gold standard, and performance often varies depending on the region of interest⁵⁴. Multi-product ensembles can be used to identify common features and assess uncertainty, where the ensemble average might be calculated with equal contribution from each driving atmospheric model as a key factor that explains uncertainty⁵⁴,⁵⁵ (Table S1). As modelled datasets, wave reanalyses/hindcasts are generally affected by methodological uncertainty factors, such as model resolution⁵⁶, forcing quality, parameterization⁵⁷ or downscaling methods³¹, which can lead to discrepancies in the resulting wave climatology, especially in complex orographic areas around islands and in semi-enclosed seas (see right panels of Fig. 3(a), and Figs. S2-S7). The uncertainty of wave hindcasts is bound to be larger in enclosed and marginal seas than in open oceans due to the important role of the mesoscales and submesoscale dynamics⁵⁸. Inter-product uncertainty increases for the extremes but it is still lower than the corresponding range of inter-annual variability (Figs. 3(a-b), S2, S3 and S6). The inter-product uncertainty of mean $T_m$ (Figs. 3(c)) relative to the climatological value (Fig. S6) is similar to the $H_s$ counterpart (after excluding an ensemble member that uses a different $T_m$ formulation, see Table S1 and Fig. S4). There is a general agreement in large-scale $\theta_m$ features among products (Fig. 3(d) and S5).

Tropical cyclones (TC) tend to be underrepresented in reanalysis⁵⁹,⁶⁰ due to their small-scale features, which affects the reliability of the resulting wave climate in the affected tropical areas. ERA5 underestimates TC intensities⁶¹,⁶² despite having an atmospheric horizontal resolution of 0.25°(Table S1) that can potentially capture a realistic distribution of TCs⁶³. As part of the Copernicus Marine Service, WAVERYS⁶⁴ was developed as the first global reanalysis with a fine resolution of 1/5°, and assimilation of wave directional spectra. Such high resolution makes this dataset an interesting source to study small-scale atmospheric features but the time period (1993 and onwards), together with the lack of ocean and atmospheric coupling, are limiting factors for the study of TC, as they are infrequent events sensitive to feedback processes⁶³.

Overall, wave reanalyses and hindcasts replicate coherent spatial global patterns of the main wave statistics, but special caution is needed in assessing trends as different models exhibit striking trend discrepancies⁵⁵,⁶⁵⁻⁶⁹ (Fig. 2(b) and S6-S7). This disagreement is arguably related to the presence of temporal inhomogeneities due to the increasing amount and type, as well as varying quality of observations assimilated over time⁶⁵,⁶⁷,⁷⁰. Model accuracy potentially increases over time (reflected by a decrease in the inter-product uncertainty over time as illustrated in Fig. S9), which is not optimal for climate research and, in particular, trend assessment. For example, the number of observations assimilated in the ERA5 wave reanalysis⁷¹ increased from approximately 0.75 million per day in 1979 to around 24 million per day by the end of 2018⁷². Additionally, temporal inhomogeneities are seen as more pronounced in the 90s and early 2000s (see Fig. S9), which relates to the assimilation of wave data from satellite altimeter missions starting in 1991 (Fig. 1), and the marked increase in the quantity of assimilated $H_s$, wind and surface pressure data in the following decade⁶⁵,⁷². Trends calculated from CFSR⁷³-derived wave products are markedly more negative than the other products (Fig. 2) because CFSR winds have a marked step change in 1994⁶⁹ (with a notable overestimation of winds before that) which coincides with the assimilation of new surface wind data⁷⁰,⁷⁴. Without considering CFSR-derived products the areas of robust signal increase (Fig. 2(b)).

Long-term century reanalysis products also have marked temporal inhomogeneities, with a notable difference in ingested data between the first and the second half of the 20th century⁶⁷. Modelled data without assimilated observations presents value for trend analysis and signal detection and attribution⁶⁶,⁶⁷,⁷⁵,⁷⁶ in that they are not affected by temporal inhomogeneities in employed observations. Furthermore, unconstricted models without data assimilation offer the possibility to generate Single Model Initial-condition Large Ensembles (SMILE), which can help investigate the internal climate variability and contribute to a more robust assessment of trends and low-frequency extremes⁶⁶,⁷⁵.

## Future wave climate

Since 1992, the IPCC has released sets of emission scenarios to be used for driving global climate models to develop climate change projections. These projections are usually carried out in the collaborative framework of the Coupled Model
Intercomparison Project (CMIP), which is developed in phases to foster climate model improvements and to support national and international assessments of climate change. The climate projections of the latest phase, CMIP6<sup>77</sup> (released in 2019) are based on the Shared Socio-economic Pathways (SSPs)<sup>78</sup>, with focus on SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5.

However, most climate models do not provide information about waves (although there are a few exceptions<sup>79</sup>). To fill this gap, the impacts of global warming on ocean wind-wave characteristics have been explored by exploiting surface wind fields (and sea-level pressure) from global and high-resolution regional climate models as forcing for global and regional wave models (typically phase-averaged models based on the spectral action balance equation<sup>2</sup>), or as a statistical predictor to simulate wave fields<sup>34</sup>. While (physics-based) wave models can include complex wave interaction processes (for example, wave-ice interaction) and are able to reproduce mixed sea states better, statistical models have low computational cost and offer the advantage of flexibility in the choice of predictors (surface winds derived from climate models have typically low skill<sup>80</sup>, and sea-level pressure gradients might be used instead as geostrophic wind proxies). Most of these wave modelling products provide only a few set of integrated wave parameters such as $H_s$, $T_m$ and $\theta_m$ (see Box 1), having the impact of climate change on wave spectral parameters not been extensively studied yet<sup>81,82</sup>.

The need to conduct a posteriori wind-wave simulations leads to limited availability of future wind-wave projections and, consequently, lower confidence of future changes in wind-waves in comparison with many other climate variables<sup>27,39</sup>. In addition, there is typically a delay between the release of climate projections from a CMIP phase and the corresponding derived wind-wave climates. While a few CMIP6-derived wave projections have been published already<sup>79,83-85</sup>, most of the state-of-the-art published literature is still based on the CMIP5 phase<sup>86</sup> and the Representative Concentration Pathways (RCP) scenarios<sup>86</sup>, with particular focus on the medium-stabilizing forcing scenario RCP4.5 and the high-emission scenario RCP8.5 (see Tables S2-S8).

Computational cost is an important factor for the generation of large ensembles<sup>66</sup>, which are key to properly account for the main sources of uncertainty, namely, internal climate variability, climate model and wind-wave modelling approach, and forcing uncertainty derived from the greenhouse gas emission scenarios. Large ensembles over long enough time periods are also beneficial for a better characterization of extreme waves driven by rare but hazardous events, such as tropical cyclones (TC). However, most climate models have spatial resolution ranging from ~250 km in the atmosphere to ~100 km in the ocean, which cannot well capture TC genesis<sup>87</sup>, intensity, frequency and variability, which makes the resulting global projections of extreme waves in TC regions uncertain<sup>63</sup>. Consequently, CMIP5<sup>88</sup> models have shown limitations in their ability to reliably represent inter-annual and inter-seasonal variability particularly within TC-affected regions<sup>80</sup>. Wave projections obtained with high resolution climate simulations (~25 km or less) provide a more realistic overall distribution of TC-driven events<sup>63,89,90</sup> but there are still large uncertainties due to the lack of feedbacks, and errors in the wind fields<sup>63</sup>. The CMIP6 endorsed High Resolution Model Intercomparison Project (HighResMIP)<sup>91</sup>, with a coordinated set of experiments with at least 50 km resolution in the atmosphere and 0.25° in the ocean, provides valuable climate data to better assess historical and future TC properties<sup>87</sup>. However, the existing wind-wave literature exploring such projections is still extremely limited<sup>85,92</sup>.

The current knowledge of future projections of wave climate at a global scale was consolidated with the development and analysis of the first coherent, community-driven multi-method ensemble of historical and future global wave simulations<sup>35-37</sup>, that resulted from a collaborative international effort in the framework of the COWCLIP project<sup>28</sup>. This CMIP5-driven large ensemble accounted for dominant sources of uncertainty<sup>35</sup> and has become a reference for the IPCC Special Report on the Ocean and Cryosphere<sup>93</sup> and IPCC AR6<sup>39</sup>. One important conclusion was that, generally, climate model-driven uncertainty dominates<sup>35</sup>, which indicates the need for further model improvement. However, the internal climate variability was not properly sampled, and only two greenhouse emission scenarios were considered<sup>35</sup> (RCP4.5 and RCP8.5). Moreover, most global wave projections used to derive this large ensemble did not include the Arctic Ocean<sup>94</sup> despite being a hotspot for wave climate change with potential dramatic increases in wave energy due to sea ice decline<sup>95,96</sup>. The existing limited literature regarding CMIP6-derived wave projections<sup>79,85,97</sup> indicates better performance for the historical period when compared to ERA5<sup>85</sup>. Projected patterns of change obtained for SSP5-8.5 are similar to those obtained for RCP8.5<sup>35,85</sup>. However, more model combinations and further testing with more hindcast/reanalysis products are advisable to derive robust conclusions, considering uncertainties in contemporary<sup>54</sup> and future<sup>35</sup> $H_s$ estimates.

At regional scale, the European-focused projects PRUDENCE<sup>98</sup> and ENSEMBLES<sup>99</sup>, which ended in 2004 and 2009, respectively, where one of the first large-scale collaborative frameworks to develop regional projections to address the need for climate change information for use in impact and adaptation research. These initiatives were followed by the international Coordinated Regional Climate Downscaling Experiment (CORDEX) that provided the framework for downscaled CMIP5 datasets at resolutions ranging from 0.22° to 0.44°, which presents added value over the coarser resolution counterparts<sup>100</sup>. CORDEX CMIP6 atmospheric projections are expected to become available between 2023 and 2024 but, as for the previous CORDEX phase, wave information is not included. An additional shortcoming is that CORDEX domains are not tailored for ocean modelling research and, for example, do not cover several parts of the world oceans.
The first regional papers investigating the future wave climate mostly focused on the North Atlantic Ocean and the Mediterranean Sea (Fig. S10), in a similar fashion as for the historical wave climate. Despite the steady increase, the existing literature still unevenly covers the world oceans/seas without necessarily focusing on the coastal regions with most population on vulnerable land to coastal flooding (defined as land below the local high tide¹⁰¹) under present and future conditions¹⁰¹ (Figure S11). Most of peer-reviewed regional scale literature is based on the RCPs (RCP4.5 and RCP8.5), and previous scenarios (A1B, B1, B2), with very limited CMIP6-derived regional projections¹⁰²⁻¹⁰⁴ (Table S2-S5), and some of them assuming simplified boundary conditions¹⁰².

In the late 2010s, news ways to present future projections and uncertainty were introduced. Climate projections have been assessed as a function of global warming above the preindustrial level, instead of using temporal and emission dependence. This perspective helps to investigate the benefits to limiting global warming, which became more relevant after the Paris Agreement of 2015¹⁰⁵ proposed to limit the increase in global warming to below 2.0° C, and preferably to 1.5°. However, this global warming level approach cannot be used with sea level rise projections as it does not correlate well with global mean temperature increase alone. There is very limited literature of projected changes in wave conditions as a function of warming levels¹⁰⁶ which can be explained by the limited amount of century-scale simulations of wave parameters that is needed to perform such an assessment. An alternative approach to represent uncertainty was introduced with the use of storylines¹⁰⁷ that are defined as physically-consistent and plausible future events or pathways that provide an actionable risk perspective. It is however a challenge to align this approach with the traditional model ensemble-based probabilistic approach, which might require changes in physical modeling to support the storyline approach¹⁰⁸. This approach has, however, not been applied yet to assess the uncertainty of future wind-wave conditions.

## Historical and future wind-waves by ocean basin

The impact of global warming on wind-waves varies across the global oceans. This section describes the historical and future wind-wave conditions for six major ocean basins: the Atlantic Ocean (including the Mediterranean Sea), the Pacific Ocean, the Indian Ocean, the Arctic Ocean, and the Southern Ocean. This review combines existing evidence from global to regional scale studies, and highlights the relative importance of the challenges introduced in the previous section. The description is articulated around four main aspects: climatology, historical trends, responses to large-scale teleconnection patterns, and future changes. Future projections focus on the changes by the end of century with the RCP8.5 scenario as this forms the largest body of state-of-the-art literature on wave climate changes. Whenever possible, changes are described for mean conditions, high-frequency extremes (90th to 99th annual percentiles) and low-frequency extremes (multi-decadal return periods).

### The Atlantic Ocean (and the Mediterranean Sea)

#### Climatology

Visual and instrumental $H_s$ observations acquired on weather ships operating in the North Atlantic Ocean from the late 1940s until the 1970s provided the first decadal records of mean annual $H_s$⁴⁰, which revealed a large variability across the whole Atlantic basin with inter-annual fluctuation of the same order as seen for the seasonal fluctuation¹⁰⁹. Increasingly available wave records in the North Atlantic have enabled extended focused analysis in this region¹¹⁰⁻¹¹³, showing a latitudinal gradient of the mean $H_s$ and its inter-annual variability (Fig. 3(a)). Maximum $H_s$ values have been recorded between Greenland and Europe (for example, the Quirin storm in February 2011 produced a $H_s$ of 20.1 m¹¹⁴, the largest recorded by satellite altimeter) and minimum values are exhibited in the Tropical Atlantic (Fig. 3(b)).

Due to a lack of in situ observations (Fig. 1), wave climate analyses in the South Atlantic are essentially based on model reanalyses¹¹⁵ (Fig. 3) and satellite data²⁹,³² (Fig. S1). The South Atlantic annual mean $H_s$ (and its inter-annual variability) also exhibits a poleward positive gradient (Fig. 3(a)) but the annual maximum $H_s$ is lower than the North Atlantic Ocean counterpart (Fig. 3(b)). The annual mean $T_m$ climatology is larger over the Southern Atlantic Ocean, and, particularly, over the Eastern side of the ocean basin due to the swell influence (Fig. 3(c)). In the extra-tropics, there is a mean westerly flow (waves coming from the west to the east) that rotates clockwise(anticlockwise) on the lower latitudes of the Northern(Southern) Atlantic Ocean, leading to the dominance of easterly waves over the Equator (Fig. 3(d)).

The Mediterranean Sea presents a more moderate wave climate, with complex spatial patterns associated with local circulation, complex orography, and fetch-limited conditions¹¹⁶,¹¹⁷. The highest recorded wind-waves in the Mediterranean are located in the Northwest Mediterranean Sea¹¹⁸, where there is also the largest inter-annual variability¹¹⁹. For example, a record-breaking $H_s$ of 8.44 m was observed by a buoy during Gloria storm in January 2020 off the Spanish coast¹²⁰.

#### Historical change

Annual mean and extreme $H_s$ trends in the North Atlantic Ocean computed over decadal time periods mostly reflect the phasing with climate oscillations, with increasing and decreasing trends in the North East Atlantic over the 1950s-1990s¹²¹⁻¹²⁵ and 1990s-2020s⁴⁴,⁶⁴ periods, respectively while North West Atlantic trends were positive over the 1990s-2020s⁴⁴,⁶⁴. The mean $H_s$
trends over the 1990-2020s lie within ± 1 cm/year but larger values in grid cells close to land and sea ice margins are exhibited by altimeter data<sup>44,64</sup>. For the 1950s-1990s period, observed trends range 0.5-3.4 cm/year for the mean $H_s$<sup>125</sup>. Several century scale $H_s$ reconstructions based on atmospheric reanalysis indicate a general increase of the annual mean and extreme $H_s$ over the 20th century<sup>67,126</sup> but these results are severely impaired due to the increasing number and changes in assimilated data<sup>67</sup>. Contemporary reanalysis/hindcast products show regional discrepancies for the North and Tropical Atlantic annual mean $H_s$ trend over the 1980-2014 (Fig. 2(b))<sup>127</sup> but a robust increase is obtained for the summer mean $H_s$ and high-frequency $H_s$ in the Tropical Atlantic with regional averages of 0.5 cm/yr and 0.7 cm/yr, respectively<sup>55</sup>. Altimetry-based $H_s$ winter trends over the North Atlantic Ocean starting 1993 are mostly caused by internal variability<sup>128</sup>.

In the Southern Ocean, multi-decadal trends computed from altimeter data from the 1992-2018 period exhibit significant positive trends of the annual mean $H_s$ in areas between 30-60°S (up to 3 cm/year) but discrepancies among satellite products are generally present in this basin<sup>44</sup> (Fig. 2). Contemporary reanalysis show a similar positive pattern for the annual mean $H_s$ (but with lower trends, Fig. 2(b))<sup>44</sup>, and an overall increase of the mean $T_m$ during the austral winter exceeding 0.01 s/yr<sup>55</sup>.

In the Mediterranean Sea, model reanalyses indicate an overall decrease of the annual mean $H_s$ over the period 1958-2001<sup>129</sup>. Altimeter data and contemporary reanalysis indicate a significant increase in the western Mediterranean Sea after the early 1990s<sup>44,119</sup> (< 3 cm/yr) which is linked to increased winter extremes<sup>119</sup>.

## Response to teleconnections

The North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) are leading modes of interannual North Atlantic wave climate variability<sup>130</sup>, showing negative correlation with winter wave climate statistics (mean and extreme) in the southern North Atlantic and positive correlation northward of 50° N<sup>52,131</sup> (Fig. 4, Figs. S12-13). The East Atlantic (EA) and Scandinavian (SCAND) patterns are also relevant atmospheric modes for the North Atlantic Ocean<sup>132</sup>, which govern winter wave activity towards more southern latitudes and contribute to larger wind-waves over the most western coasts of Europe during their positive phase (Fig. 4(a)). A negative phase of SCAND also contributes to larger $H_s$ in the northern North Atlantic, including the North Sea (Fig. 4(b)). The Western Europe Pressure Anomaly (WEPA) has been shown to explain 40-60% of observed winter-averaged $H_s$ (mean and extreme) variability off western Europe<sup>133</sup>.

The Tropical and South Atlantic wave characteristics are poorly correlated to most climate variability patterns<sup>134</sup> (Fig. 4). However, the Atlantic Multidecadal Oscillation (AMO) is strongly correlated (at decadal time scales) to increased mean wave power within most South Atlantic regions<sup>135</sup>. Also, a 3000-year reconstruction of changes in predominant wave direction in a Brazilian coastal location (based on coastal morphology changes preserved in beach-foredune ridges) indicates that the Southern Annual Mode (SAM) is a primarily driver for multi-centennial cycles in $\theta_m$<sup>136</sup>.

In the Mediterranean Sea, the interannual variability of extreme waves in winter is dominated by the negative phase of the EA with a larger effect in the western basin (Fig. 4(b)). Additionally, a positive SCAND indicates larger (smaller) heights in the western(eastern) Mediterranean Sea<sup>137</sup> (Fig. 4(a)). The winter average $H_s$ is also anti-correlated with the winter NAO<sup>129</sup>. However, while large scale patterns influence the Mediterranean wave field, the wave dynamics in the Mediterranean are strongly influenced by the regional orographic conformation and fetch, which acts as filter to favor atmospheric circulation components that are more effective in producing waves due to the basin configuration<sup>129</sup>.

## Future projections

There is strong consensus towards decreasing mean $H_s$ (0-10%) (Fig. 5), $T_m$ (0-5%) and wave energy (0-5%) across much of the North Atlantic<sup>35,138,139</sup> (Figs. 5 and S14-15). This decrease is statistically significant for both RCP4.5 and RCP8.5 but it is more intensified for the latter (up to ~5% vs. up to ~10% $H_s$ change for the low and high emission scenarios, respectively)<sup>35</sup>. High-frequency $H_s$ extremes are (overall) projected to decrease (0-10%), but such changes are not robust amongst models and assessments<sup>140</sup>. Multi-model ensemble projections of 100-year return period $H_s$<sup>140</sup> exhibit a projected increase for sub-arctic regions and the South Atlantic Ocean (0-20%), where there is also a projected increase in energy flux >10%<sup>141,142</sup>.

$\theta_m$ is projected to shift clockwise (up to 10 degrees) for most North Atlantic areas and anticlockwise (up to 10 degrees) for high-latitude areas (>50° N). These changes are consistent with a projected decrease in future mid-latitude storm activity, driven by a projected northward shift of North Atlantic storm tracks to higher latitudes, on top of more frequent atmospheric blockings<sup>138</sup>. The projected signal of change in wave characteristics for the tropical Atlantic regions is uncertain<sup>34,35</sup> (Fig. 5), except for $\theta_m$, which shows a consistent clockwise rotation of up to 10 degrees. In the South Atlantic, small projected future increases in extreme $H_s$ and $T_m$ values have been obtained but they are not consistent amongst models and assessments<sup>34,35</sup>.

Projections using high-resolution atmospheric forcing fields (with a better representation of hurricane events) show that the annual maximum $H_s$ is projected to decrease off North America but increase (up to 0.5-1 m) along South America and North Europe's Atlantic coast under RCP8.5<sup>89</sup>. However, the projected 20-year return period of $H_s$ varies widely along North America's Atlantic coast and the Gulf of Mexico and highly depends on forcing resolution<sup>63</sup>. CORDEX-based single-model simulations downscalled along the European coastlines show decrease in the mean $H_s$ (~10%) but (a less robust) increase (~1 m) in the annual maxima resulting from a widening of the probability distribution<sup>143</sup>.
In the Mediterranean Sea, global and regional future projections show a general decreasing trend in mean $H_s$ (0-10%), $T_m$ (0-5%) and wave energy$^{35,144-146}$ (Fig. 5), with a slight eastward shift in $\theta_m^{144}$ and an increase in multimodal wave climate$^{146}$. However, in some localized energetic areas, such as the Northwestern Mediterranean, mean and extreme waves might increase$^{147}$. For example, a multi-model assessment of the $H_s$ associated to Mediterranean Hurricanes shows that their 100-year return period is projected to increase around Balearic Islands and Sicily ($<10%$)$^{148}$.

## The Pacific Ocean

### Climatology

The Pacific Ocean historical wave climatology and its relevant extreme statistics have been described using multi-decadal model hindcasts or reanalyses$^{68,149}$ complemented by satellite altimeter-based records$^{150}$, ship observations$^{151}$, and regionally focused buoy data assessments$^{45, 110, 152, 153}$. Within mid to high-latitude areas ($>45°$ N and $<45°$ S), there is a well-documented unimodal wave climate$^{154}$ driven predominantly by Northern and Southern Hemisphere mid-latitude storm systems with temporally-averaged wave energy and $H_s$ reaching their peaks. The largest annual mean $H_s$ occurs in the mid-latitudes of the Southern Hemisphere, while the annual maxima takes place in the Northern Pacific Ocean, exhibiting a similar latitudinal gradient as the Atlantic Ocean (Fig. 3). For example, the strongest storms in the Eastern North Pacific have generated $H_s$ in the range of 14-15 m$^{153}$.

The North and South Pacific extra-tropical areas show large seasonality and inter-annual variability (Fig. 3). Within equatorial tropical regions ($>30°$ S to $<30°$ N), a complex multi-modal wave climate prevails almost everywhere (driven by remotely-generated swells and higher-frequency waves generated by prevailing trade winds)$^{154}$ and temporally-averaged wave energy and $H_s$ exhibit relatively lower values. The Southern Ocean generated swell is a dominant influence, particularly in the south-east Pacific Ocean, where the annual mean $T_m$ largely exceeds 10 s (Fig. 3(c)). The Pacific islands possess a wave energy resource of high interest to wave energy developers, owing to its high power and low variability$^9$.

### Historical change

Satellite altimeter data shows that North Pacific displays statistically significant negative trends in the annual mean $H_s$ ($< 1$ cm/year) between 1985-2018 (Fig. S1), despite mean wind speed showing no clear trends across these basins$^{32,44}$. Similar negative trends are also obtained in parts of the North Pacific Ocean by some contemporary reanalysis/hindcast products for 1980-2014 (Fig. 2). In the sub-tropics, contemporary reanalysis/hindcast products show a clockwise rotation of $\theta_m$ during winter season. Following adjustments to correct for inhomogeneities in buoy records, slightly positive significant trends in mean $H_s$ are observed off North California and negative trends off Alaska and British Columbia but no significant trends were found in extreme $H_s$$^45$. In the western North Pacific, the observed wave energy by buoys increased significantly on the Pacific side of eastern Japan over the period 1980-2009, in agreement with modern reanalysis$^{155}$ (Fig. 2). Altimeter-derived trends exhibit non-significant positive values for high-frequency extremes, such us the 90$^{th}$ percentile, for specific northern regions ($>1$cm/year) and gradually become more negative further south (-0.3 cm/year). For 1991-2015, satellite data shows consistent $H_s$ increases (0.56 cm/year and 1.25 cm/year for the mean and 99$^{th}$ percentile, respectively) in the Northwest Pacific and Japan Sea$^{156}$. However, these extreme $H_s$ trends can be affected by the undersampling impact on altimeter derived trends$^{47}$.

A regional reconstruction of $H_s$ between 1911-2010 shows that seasonal maximum values appear to have increased during summer and spring over the central South China Sea and during summer for the East China Sea ($>2$cm/year), although trends are predominantly negative across both regions$^{157}$. No trends in mean $H_s$ are observed in the tropical Pacific$^{32,44}$ for either mean or high frequency $H_s$ extremes over the periods 1985-2018 and 1992-2017, with modern reanalysis showing inconclusive results there$^{44}$ (Fig. 2).

In the South Pacific, the altimeter record shows no clear trend for the annual mean $H_s$ over 1985-2018 except in the Southwest Pacific, where trends are statistically significant negative ($<1$ cm/s, see Fig. S1), whereas there is a significant positive trend (0.5-1 cm/year) for high-frequency $H_s$ extremes (90$^{th}$ percentile)$^{158}$. Conversely, wave reanalysis/hindcast show a consistent increase in the annual mean $H_s$ over the Southern Ocean that exceeds 1 cm/s (except for CFSR-derived products) (Fig. 2), which relates with an increase in the mean and high-frequency $H_s$ extremes during the austral winter$^{55}$. Analysis of buoy records along Australia's east coast display small significant positive trends in the north (Coral sea coast), and small significant negative trends in the south (Tasman Sea coast) (with absolute magnitudes $<0.5$cm/year)$^{159}$.

### Response to teleconnections

The Pacific Ocean region is strongly influenced by recurring patterns of atmosphere-ocean climate variability which force anomalous atmospheric and ocean wind-wave characteristics at inter-annual to multi-decadal time-scales$^{160}$. The El Niño Southern Oscillation (or ENSO) is a key pattern of Pacific inter-annual climate variability, with its extreme phases (El Niño and La Niña events) strongly linked to anomalous spatial and temporal wind-wave characteristics$^{16}$. The Southern Oscillation Index (SOI) gives an indication of the development and intensity of El Niño (negative values of the SOI) or La Niña events (positive values of the SOI) in the Pacific Ocean. CMIP5 models can on average capture the major observed mean and extreme $H_s$
responses to ENSO¹⁶¹. Satellite altimeter-based records and model data show that El Niño events are associated with elevated wave energy levels and increased $H_s$ over the south-west tropical and Northeast Pacific regions (see Fig. 4(b)), and reduced wave energy within Northwest Pacific regions¹⁴, ⁵¹, ¹⁴², ¹⁶¹, ¹⁶². In contrast, La Niña phase events have been linked to elevated wave energy levels and $H_s$ values for most South and Northwest Pacific regions⁵¹, ¹⁶². The ENSO also affects $\theta_m$ with El Niño events forcing anticlockwise (southerly) /clockwise (southerly) rotations across Northeast / Southwest Pacific regions¹⁴, ¹⁶².

Extreme Pacific Decadal Oscillation (PDO) phase events lead to similar spatial patterns on multi-decadal time-scales but reduced wave energy flux anomalies relative to ENSO events¹⁶². High wave intensity is experienced over most Northeast Pacific regions during PDO warm (positive) phase (see Fig. 4(a)) and decreased wave intensity is more common during PDO cool (negative) phase¹⁶². The Pacific-South American and Pacific-North American (PNA) modes have also been correlated with South and North Pacific Ocean swell waves generated, respectively, that travel equatorward⁵³. Significant increases in extreme $H_s$ over central North Pacific areas are found to be connected with a deeper and eastward extended Aleutian low⁴⁴.

## Future projections

Across the North Pacific, tropical Northwest Pacific and extra-tropical South Pacific regions, global scale projections exhibit a strong agreement that annual and seasonal mean $H_s$ will decrease (5-10%) by 2100 under RCP8.5³⁵ (see Figs. 5 and S14). This decrease relates to a decreased north-south pressure gradient and wind speed³⁵, ¹⁶³. Single-model regional projections over the East China Sea show similar projected decreases for the mean $H_s$ but wind-sea dominant $H_s$ high-frequency extremes are projected to increase (>10% in summer), which are likely related to projected changes in the local winds¹⁶⁴. Fewer large wave events are also projected for eastern Australia (-42% for RCP8.5)¹⁶⁵. In contrast, tropical East Pacific areas exhibit robust positive projected changes for annual mean $H_s$ (up to 5% for RCP8.5 and up to 3% for RCP4.5) and annual number of high-frequency wave storms (up to about 25-50%)³⁷. Robust increases in 10-year return $H_s$ up to 15% are also seen in the tropical Pacific for a 3°C warming level (which occurs in the range of years from mid to the end of the century for RCP8.5 scenario)¹⁰⁶. This projected increase in $H_s$ is mainly attributed to the projected increase in southeasterly Pacific trades³³, ¹⁶⁶ and is associated with an El Niño-like mean circulation intensification¹⁰⁶. Analysis of projected change in the spectral characteristics indicates the swell energy from the Southern Ocean is also a major contributor to this increase⁸².

In terms of typhoon-driven extreme $H_s$ (with a probability of occurring once every ten years), wave ensemble projections show changes ranging 30% for Northwest Pacific regions (positive changes around Japan and negative changes for Southeast China Sea regions) owing to a future eastward shift of typhoon tracks⁸⁹. However, these estimates are affected by large uncertainty levels associated with typhoon intensity and track projections. There is also uncertainty regarding how TC-driven waves will change around Pacific Islands as different projections exhibit a large range of possible variations¹⁶⁷. Projections in the upper tail of the $H_s$ distribution are unclear nearly everywhere³⁴, ³⁵, yet ensemble projections of 20-year¹⁶⁶ and 100-year return period $H_s$¹⁴⁰, ¹⁶⁸ show a projected increase for sub-arctic regions (5-10%) and a projected decrease across South and tropical Northwest Pacific regions (5-10%).

In terms of the annual mean $T_m$, there is a projected decline for Northwest and Southwest Pacific areas (up to 5%) and a projected positive change for East Pacific regions (up to 5%)³⁵, ¹⁶⁸ (Fig. S15). An extended energy increment of <10% (for 100-year energy flux) is projected throughout the subequatorial-tropical and north-eastern Pacific Ocean partly due to increased swell influence¹⁴². Mean $\theta_m$ are projected to change clockwise over sub-tropical and tropical regions and anti-clockwise at high-latitudes (5°-10°)³⁵.

## The Indian Ocean

### Climatology

Historical climatology in mean and extreme $H_s$ have been analysed based on ship-reported wave data¹⁶⁹, ¹⁷⁰, in-situ buoy data¹⁶⁹, ¹⁷¹, ¹⁷², hindcasts¹⁷³⁻¹⁷⁷, reanalyses⁶⁵, ¹⁷⁸⁻¹⁸⁰, and satellite altimeter data³², ⁴⁴, ¹⁸¹⁻¹⁸³. As exhibited in other basins, a poleward positive gradient in mean $H_s$ and its interannual variability is found across the Indian Ocean (Fig. 3(a)). The Indian Peninsula/subcontinent divides the North Indian Ocean (0-30°N) into two basins: the Arabian Sea to the west, and the Bay of Bengal to the east. The dominant feature of the North Indian Ocean is the monsoon winds, which reverse direction annually and are an example of intense ocean-atmosphere interaction at basin scales¹⁸⁴.

In the South Indian Ocean, the extratropical westerly winds dominate. Strong seasonal signals are observed in both mean and extreme $H_s$ year-round, with a peak during June-August¹⁴, ¹⁸⁵. The Southern Ocean swell is a dominant influence, that propagates northwards across the basin to impact on the coasts of the Indian Peninsula/sub-continent (and islands)¹⁴ (Fig. 3(c)). For example, in May 2007 southern swell that originated around 40° S impacted Reunion Island with $H_s$ > 6 m, as recorded by altimeter data. The climatological mean value of $T_m$ presents high values in the entire domain except the eastern Arabian Sea, where wind sea states are more dominant¹⁸³, ¹⁸⁶⁻¹⁸⁸ (Fig. 3(c)). Like the Pacific islands, the islands in the South Indian Ocean are locations of interest in relation to their potential for wave energy extraction⁹.
## Historical changes

Contemporary hindcasts/reanalysis products (without considering CFSR-derived products) agree in a robust positive mean and extreme (90th percentile) $H_s$ trend for a large fraction of the Indian Ocean over 1985–2015 for the months of December to February (with an average of ~0.4 cm/year and ~0.6 cm/year, respectively, over the areas of positive increase)⁵⁵. Modeled data also shows a mean $T_m$ increase during winter in the Southern Indian Ocean⁵⁵. The seasonal $H_s$ increase is reflected in a positive annual mean trend¹²⁷ in the Southern Indian Ocean with a rate <0.4 cm/year (Fig. 2). Different altimeter data products show conflicting signals over latitudes north of 30° S for the period 1992-2017⁴⁴. Available merged altimeter $H_s$ data for the 1985-2018 indicates non-significant trends for both mean and high-frequency extremes north of 30° S, while a large area with positive trend (>1 cm/yr) is depicted south of 30° S³².

Seasonal analysis of individual wave reanalysis depict a large increase in $H_s$ (~1.2 cm/yr) over the North Indian Ocean during the summer monsoon period as compared to other seasons¹⁸³, ¹⁸⁵, ¹⁸⁶. Single product assessments also exhibit declining regional trends of the 90th percentile winds in the Arabian Sea¹⁸⁰ and increasing trends in the central Bay of Bengal¹⁷⁶ for the period 1979-2012, with corresponding influence on the locally generated sea (0.2 cm/year). However, an ensemble of contemporary hindcasts/reanalyzes shows little changes for the North Indian Ocean $H_s$ statistics⁵⁵.

## Response to teleconnection patterns

Natural climate variability such as ENSO, the Indian Ocean Dipole (IOD), and the Southern Annular Mode (SAM) exert significant impacts on wind and wave climate over the Indian Ocean⁵¹, ¹¹⁸, ¹⁸⁵, ¹⁸⁸–¹⁹¹. In the summer monsoon, El Niño amplifies the tropical cyclone activities in the Bay of Bengal leading to a significant increase in $H_s$ there¹⁸⁵, ¹⁹². In contrast, in December to February, El Niño weakens the tropical Walker cell and trade winds and thus reduces $H_s$ over the Tropical Indian Ocean¹⁶¹, ¹⁹³, ¹⁹⁴. Monsoon-driven winds and Boreal Summer Intra-Seasonal Oscillation (BSISO) modulate the wave activities in the Tropical Indian Ocean during the summer monsoon¹⁹⁵. The positive IOD events decrease $H_s$ in the Arabian Sea due to the change in the direction of wind patterns during September-November¹⁸⁵, ¹⁹⁶. Further, the SAM being a dominant mode of the Southern ocean not only affects the wave climate over the Southern Indian Ocean but also drives changes over the North and Tropical Indian Oceans year-round¹⁸⁵. Intra-seasonal variation of surface zonal wind induced by the Madden Julian Oscillation (MJO), that traverses eastward from the western tropical Indian Ocean to the eastern tropical Pacific, is associated with anomalies in $H_s$, $T_p$ and wave energy flux¹⁹⁷.

## Future projections

The projected wind-wave climate in the Indian ocean has been assessed from both global and regional studies³⁴, ⁹⁴, ¹⁹⁸, ¹⁹⁹. Seasonal mean and high-frequency extreme $H_s$ increases up to 10% and 20%, respectively, are projected over areas of the North Indian Ocean during all seasons other than December to February, and over the western Tropical Indian Ocean during the months from June to November in line with the projected circulation change towards an IOD positive phase-like mean state¹⁶¹ (under the RCP8.5 scenario). Winter mean $H_s$ exhibit a robust decrease over the western Indian Ocean from 30°N to 30°S (up to 10%)³⁵. However, areas of statistically significant increases (<20%) of 100-year return levels are projected¹⁴⁰. The annual mean $T_m$ shows robust increases in the North Indian Ocean (<5%) (Fig. S15) due to an increase of the Southern Ocean swells³⁵, ⁸¹, as well as a countercloakwise rotation in the western side of the basin (up to 5°)³⁵.

The Southern Indian Ocean displays relatively consistent signals of projected change of the mean $H_s$, with increases in high-latitudes and decreases in mid-latitudes (<5% for RCP8.5) throughout the year (see Fig 5), which is related to future change in SAM toward its positive phase¹⁶¹. 20-year return period are projected to increase in the high-latitudes and eastern mid-latitudes¹⁴⁰, which also increased mean $T_m$ due to increased southern swell influence⁸¹. Additionally, the assessment of changes in spectral characteristics⁸¹, with emphasis on the extremes²⁰⁰, shows zones of projected decrease in annual mean $H_s$ in the southeast Indian Ocean, associated with the projected future southward shift in westerly winds in the region²⁰¹.

On a regional scale, future projections of wind-wave climate have been assessed mainly in the North Indian Ocean. Along the Indian coasts, annual mean $H_s$ has been projected to increase by up to 30%, and wave periods of 20% and 10% on the east and west coast, respectively¹⁸⁰. On the west coast, 100-yr return periods $H_s$ have been projected to increase between 5 and 58%²⁰². Projected increases in $H_s$ of 5% around Reunion island have been suggested, associated with a 6.5% increase in the intensity of cyclones in the region²⁰³. In the Persian Gulf, a future decrease in wave power (up to 40% in the northern Persian Gulf) is projected²⁰³, with both $H_s$ and $T_p$ decreasing approximately 15% and 5%, respectively, for all scenarios²⁰³, ²⁰⁴. Conversely, CMIP6-based projections indicate an increase of 21 to 45% in the Gulf of Oman future's wave power under SSP-5.8.5¹⁰⁴. Along the Indian Ocean coast of Australia, the projected increase and anticlockwise rotated offshore wave conditions have been propagated onto the coast²⁰⁵. Nearshore, the influence of future sea-level rise (SLR) on the nearshore transformations of wave climate were found to dominate any effects of projected changes in offshore wave climate on the future incident wave climate.
# The Arctic Ocean

## Climatology

The Arctic Ocean is characterized by several semi-enclosed seas such as the Barents, Kara, Laptev, East Siberia, Chukchi, and Beaufort. The largest waves occur in the Norwegian and Greenland Seas as a result of extratropical cyclones that can travel from the North Atlantic to the Barents Sea²⁰⁶. Atlantic waves also propagate northwards into the Baffin Bay Davis Strait corridor, where they typically encounter wind-sea states traveling in opposite directions²⁰⁷,²⁰⁸. The influence of waves from the Pacific on the Arctic wave climate is minimal, as the two basins are connected only by the narrow Bering Strait.

In the Arctic Ocean, wave fetch greatly depends on sea-ice extent and complex wave-ice interactions take place in the marginal ice zone, such as ice-induced wave attenuation and scattering²⁰⁹,²¹⁰. Sea ice has historically reached its minimum and maximum extents in September and March, respectively²¹¹. Seasonal sea ice forms in early to late fall, and subsequently breaks up sometime in late spring or early summer. This sea ice cover fluctuation leads to a large $H_s$ seasonal cycle, particularly in the Baffin Bay, Beaufort-Chukchi, East Siberia, Laptev, and Kara Seas²⁰⁷, where wave generation has been mostly occurring during the summer season. The wave season is, however, expanding as a result of sea ice retreat. For example, an unprecedented $H_s$ of 5 m was measured by a buoy in the Beaufort Sea in October 2015 for the first time³,²¹².

## Historical changes

The historically limited influence of wind-waves in the Arctic region, in combination with the lack of in-situ observations and complex wave-ice interaction processes, has led to very limited studies about the Arctic Ocean wave climate until the 2010s. The Arctic Ocean wave climate has gradually received increased attention as a result of Arctic sea ice extents reaching unprecedented minima in 2012 and 2020²¹³, coinciding with longer records of available altimeter data²¹⁴. The resulting increase in fetch has resulted in enhanced sea states and the emergence of swell energy notwithstanding any changes in wind magnitude, direction, and duration³,²⁰⁷.

Both hindcast data⁶⁸,²¹⁴⁻²¹⁶ and altimeter observations²⁰⁷,²¹⁴,²¹⁷ show increasing wave energy across all Arctic, with an upward trend of 1-3 cm/year for the mean $H_s$ during 1990s to 2010s, and up to 10 cm/year for high-frequency extremes (99th percentile). In particular there are wide spread increases in autumn waves, with trend strengthening in 1990s-2010s in comparison to 1980s-2010s²¹⁵,²¹⁶. Such an increase in $H_s$ cannot be explained by wind speed alone²¹⁵,²¹⁸, although there is a strong correlation between $H_s$ and wind speed²¹⁴,²¹⁹. It is, however, difficult to quantify the isolated contribution of the wind speed on wave growth due to existing feedback mechanisms between wind and sea ice.

In the Atlantic side of the Arctic that is less affected by changes in seasonal sea ice, the Norwegian Sea exhibit decreasing trends in the mean $H_s$ (~1 cm/year), which can be explained by a decrease in wind speed²⁰⁷. High-frequency $H_s$ extremes there seem to have increased and decreased during, respectively, spring and fall (~1 cm/year) but with regional discrepancies among contemporary reanalyses/hindcasts.⁶⁸. Merged altimeter data shows a significant negative trend for the mean $H_s$ in the Nordic Greenland Sea (~1 cm/year), which can be explained by a decrease in wind speed²⁰⁷.

## Response to teleconnection patterns

The AO and NAO are correlated with the Norwegian and Greenland $H_s$¹³¹,²⁰⁶,²⁰⁷, with their positive phase contributing to larger waves there (see Fig. 4(a)). The decreasing trend in NAO is expected to have caused the decreasing trend in the wave extremes of the Atlantic side of the Arctic that is not affected by sea ice²⁰⁷,²²⁰. PDO is negatively correlated with mean and extreme $H_s$ in the Barents Sea over the last two decades (1992-2014)²⁰⁷,²¹⁷. Differently, a weak positive correlation is found between PDO and the Beaufort-Chukchi Seas, which is arguably caused by the strengthened Easterly winds when PDO transitions into a positive phase that flow parallel to the ice edge in this region²⁰⁷.

In the inner Arctic, historical observations and future projections seem to indicate a weakening of the Beaufort High, which seems to relate to a pan-Arctic intrusion of North Atlantic cyclones favoured by sea ice retreat²²¹. In 2017, an intrusion of low-pressure systems from the North Atlantic, along the East Siberian coast, into the Arctic basin, produced a collapse of the Beaufort High, which featured an anomalous reversal of the normally anticyclonic surface winds and sea ice motion in the western Arctic²²¹.

## Future projections

It has become evident that the Arctic is a hot spot for global climate change. Climate warming is amplified in this region, with air temperatures rising at least three times as fast as the global mean²²²,²²³. Sea-ice loss is a key driver of this enhanced Arctic warming, driving positive feedback, or so-called Arctic Amplification²²⁴. In addition, there is growing evidence that waves can contribute to this positive feedback mechanism by means of sea ice breaking and melting²⁰⁹,²¹²,²²⁵, but this has not been properly quantified to date.

The reduction of sea-ice extent and lengthening of the open water season, together with changes in surface winds, leads to projected increases in waves much larger than any other region of the world exceeding 50% regionally and 400% locally under RCP8.5 (Fig. 5 and S14-15). Average winds over the Arctic Ocean are projected to strengthen locally by up to 50% during the
fall and winter seasons and with the frequency of extreme winds speeds doubling in some areas<sup>226</sup>. The Arctic will be virtually ice-free in September by 2050 independent of the emissions scenario<sup>227</sup>. By 2100, these combined effects result in projected widespread monthly H<sub>s</sub> increases above 70° N from July to November, with the annual maxima occurring later in the year (for example, shifting from September to November in the Beaufort Sea)<sup>95,96</sup>. A counterclockwise rotation of θ<sub>m</sub> in the Beaufort Sea might indicate a weakening of the Beaufort High. Projections of the annual maximum H<sub>s</sub> amount up to two to three-fold increase along some coasts and up to 6 m offshore in the Arctic Ocean and Greenland Sea under the RCP8.5 scenario<sup>95</sup>. While changes in winds are an important driver, they alone cannot explain the projected increases in the largest waves, as similarly observed for the historical period<sup>95</sup>.

Overall, projected increases in Arctic waves are statistically robust. However, uncertainty in the specific estimates arises from the lack of a large ensemble of Arctic wave projections that can properly cover the large inter-model and inter-scenario variability in the Arctic region—there are just a few regional assessments and most of global projections do not include the entire Arctic Ocean<sup>94</sup>. Upcoming CMIP6-based Arctic wave projections might present lower uncertainties as CMIP6 sea ice extent projections have a lower inter-model spread with more realistic estimates in comparison to the CMIP5 counterpart<sup>227,228</sup>. However, the ocean wave modelling approach presents a notable source of uncertainty in this region due to the scarcity of data, the complexity of sea ice-wave interactions, and the consequent sensitivity of wave simulations to different sea ice parameterizations<sup>95,212,229</sup>.

# The Southern Ocean

## Climatology

The Southern Ocean is defined here as the region between 40°S and 60°S, south of the continents of Australia, Africa and South America. It is unique, in that it represents a continuous body of water encircling the Earth with the only significant spatial constraints being the 1000 km wide Drake Passage between South America and the Antarctic Peninsula, and the seasonal advance and retreat of the Antarctic sea-ice extent<sup>230</sup>. The consequent long fetches, combined with continuous progression of low-pressure systems which propagate across the Southern Ocean, mean that, in addition to a sustained year-round intense wave climate, the region is also the generation source for swells influencing the wave climate of the Pacific, Atlantic, and Indian Oceans<sup>158</sup> (see Fig. 3(c,d)). Priority areas for wave power extraction have been identified over the southern hemisphere, including coastlines of New Zealand, Australia, and south of Africa.<sup>9</sup> Decadal variability of associated wave power follows that of the change in swell wave height<sup>9</sup>.

Due to the remoteness of the Southern Ocean, there are few in-situ buoy assessments of wave climate<sup>14, 158, 231, 232</sup> (Fig. 1). Global model datasets combined with satellite data are needed to characterize the Southern Ocean wave climate<sup>32, 44, 150, 186, 187, 233, 234</sup>. The long uninterrupted fetches and sustained year-round strong westerly winds of the Southern Ocean lead to an annual mean H<sub>s</sub> higher than any other ocean basin<sup>183,234</sup> (Fig. 3(a)). However, relative to similar latitudes in the North Atlantic and North Pacific, extreme wave conditions are lower<sup>67, 187, 235</sup> (see Fig. 3(b)) and seasonal variation is relatively small. While the Southern Ocean wave climate is spatially quite homogeneous with a band of high waves encircling the Earth at approximately 50°S, wave conditions are highest between Africa and Australia, and lowest to the east of the constricted Drake Passage (Fig. 3(a)). The maximum recorded H<sub>s</sub> by in-situ buoys is 12.5 m, recorded in April 2012 south of Australia, but individual waves close to 30 m might occur<sup>158</sup>.

## Historical changes

Model datasets<sup>67,127</sup> (except CFSR-derived products) and altimeter data (Figs. 3(a), S1 and S7) show broad regions of significant increasing mean H<sub>s</sub> across the Southern Ocean ranging 1-3 cm/year over 1980s to 2010s<sup>32,186</sup>, with intensified rates for the Southern Ocean Atlantic Section over 1992-2017<sup>44</sup>. This increase is associated with strengthening of the westerly winds and a migration of the low-pressure systems to higher latitudes<sup>236</sup>.

Changes in extreme wave conditions are less well understood due to limitations in both altimeter and model datasets under extreme conditions, and the scarcity of in-situ observations<sup>158</sup>. The limited data does, however, suggest an increase in the frequency and intensity of storm peaks, leading to a larger increase in Southern Ocean extremes than mean conditions<sup>14, 32, 186, 231, 232, 235</sup>, with larger extensions of positive increase exhibited for the austral summer<sup>55</sup>.

## Response to teleconnection patterns

The key mode of interannual wave climate variability in the Southern Ocean corresponds with the SAM<sup>14, 51, 53, 190</sup>, which is a dominant mode of atmospheric variability in the Southern Hemisphere<sup>237,238</sup>. The latitudinal shift in Southern Hemisphere mid-latitude westerlies moves polewards/equatorwards in its positive/negative phase<sup>239</sup>, and influences the spatio-temporal characteristics of the wave field. During the positive SAM, the stronger zonal wind over the unobstructed Southern Ocean leads to larger waves there (Fig. 4(a)), which propagate northwards and might cause positive anomalies of the T<sub>m</sub> in the Pacific Ocean<sup>190</sup>. The signature of the SAM in wind-waves thus extends beyond local wind-generated forcing in the Southern Ocean, and can affect the Northern Hemisphere extratropics, especially for the years that are not influenced by El Niño<sup>190</sup>. The
Pacific-South American modes are another important influence on the Southern Ocean wave climate, with the PSA-1 mode being positively correlated with $H_s$ variability in the southeast Pacific and negatively correlated in the Indian Ocean sector of the Southern Ocean⁵³.

### Future projections

Existing studies show consistent projected increases in the Southern Ocean wave climate, with the rate of increase larger for the RCP8.5 scenario than for RCP4.5³⁷. These projections show increases in annual mean $H_s$ by 2100 under RCP8.5 of approximately 5% (Fig 5). There is also an increase in the annual $T_m$ (3%) (Fig. S15) and a counterclockwise rotation of the $\theta_m$ of approximately 3° to 5°. Similar ensemble projections of low-frequency extreme wave conditions⁶⁷ show a projected increase in 100-year return period $H_s$ of approximately 7% for RCP8.5. Like in the tropical Pacific Ocean, there are also robust increases in 10-year return period $H_s$ up to 15% (~1m) over the Southern Hemisphere high latitudes by the end of the century, particularly at 3°C warming. These increases are associated with an increase of the SAM positive phase³⁷,¹⁰⁶. Regarding high-frequency extremes, global projections show a robust increase in the frequency and intensity of storms³⁷.

CMIP6-based single-model regional projections over the Bass Strait and south-east Australia agree to project an increase of the mean $H_s$ (7%) in the offshore regions but reveal a decrease (2%-3%) in some nearshore areas due to decreases in the local wind¹⁰³. This highlights the importance of accounting for local atmospheric and morphological conditions in assessing nearshore wave climate changes. As in the Arctic ocean, existing literature of future Southern Ocean wave projections at both global to regional scales consider simplified sea ice-wave parametrization without sea ice coupling. Wind-waves can have an important role in sea ice break up and sea ice retreat²⁰⁹, meaning current projections of sea ice retreat and $H_s$ increase near the Antartica could be underestimated.

## Regional impacts of wave climate change

The potential wave climate changes in a warmer world can in turn impact coastal communities and marine-built infrastructure. A comprehensive review of the physical impacts of changes in wave action is out of the scope of this paper but here we provide some examples that illustrate how wave climate change might exacerbate coastal vulnerability.

### Coastal damage in the Atlantic coast of Europe

During winter 2013/14, the Atlantic coast of Europe faced the most energetic and persistent extreme wave conditions of the last 67 years²⁴⁰, and many coastal damages were reported. Some of the few existing long-term beach surveys revealed unprecedented sediment loss²⁴⁰,²⁴¹, and permanent coastal change occurred along rocky coasts, with some coastal cliffs experiencing retreat rates 2 orders of magnitude greater than the long-term average²⁴². Despite the large impacts, the observed wave extremes have been mainly explained by the natural variability of the climate system¹¹³, ¹²⁵, ²⁴³ and it is still under debate whether future extreme wave conditions over Western Europe will be more or less frequent and/or intense. Yet, current knowledge of the wave climate indicates that periods of intense wave activity will continue to occur during the 21st century, and the combined impact of extreme wave conditions with increased SLR represents a major threat for densely urbanized coastal zone²⁴⁴.

### Flooding and erosion in the Pacific and Indian coastlines

Wave climatological variability associated with El Niño, along with contributions from storm surges and seasonal sea-level anomalies has been observed to be key control of coastal vulnerability for all land masses bordering the Pacific¹⁶, ¹⁶², ²⁴⁵. Extreme coastal response on the US Pacific margin has been observed with El-Niño-driven anomalies in winter wave energy and direction¹⁶. Anomalous wave directions have also been linked to extreme coastal erosion in South East Australia¹⁷. Also, storm wave-driven flooding events across the Pacific atolls have been linked with remotely generated swells from the North Pacific²⁴⁶, and most Pacific Ocean atolls will be uninhabitable by 2050 due to sea level rise exacerbating wave-driven flooding²⁴⁷. The Maldives in the Indian Ocean is similarly subject to wave-driven flooding, and flooding will become increasingly common in the region as sea levels continue to rise²⁴⁸⁻²⁵⁰.

### Impact on coastal and offshore structure design requirements

Wave climate change might impact coastal and offshore structure design requirements worldwide. In addition to sea-level rise, it is important to estimate future long-term changes in extreme water levels caused by storm surges, and wave height for coastal hazard mitigation²⁵¹. For example, TC intensity is expected to increase in the mid-latitudes of the Northern Pacific²⁵¹, and associated future projected wave height increases dictate an increase of up to 1.5 m in breakwater caisson width of a typical in Japan²⁵², ²⁵³. Similarly, a change in the design of offshore wind turbines located along the west coast of India is required to avoid a decrease in fatigue life caused by the impacts of wave climate change²⁵⁴.
## Increasingly vulnerable Arctic coastal communities

Vulnerable Arctic coastlines have traditionally been protected from marine drivers by the presence of year-round sea ice. The frequency of extreme water levels and erosion events are anticipated to rise due to the combined action of waves, rising sea levels, storm surges, tides, and intensifying permafrost degradation<sup>255,256</sup>. This combined action has a dramatic impact on the Arctic coastal ecosystems and communities, exacerbating existing vulnerability of Indigenous communities located in low-lying coastal areas<sup>95</sup>. Wave storms (for example, Fig. S15) have already caused flooding and infrastructure damage. The decreasing distance between the ocean and the coastal settlements continues to threaten homes, water resources, infrastructure, and sites of historical and cultural significance<sup>257-259</sup>.

## Robust change in the Southern Ocean with unclear impacts

The Southern Ocean exhibits some of the more robust evidence for both historical and projected future change<sup>32,35</sup>, yet the regional impacts of this change are still poorly known. Other marine drivers can exacerbate or compensate wave-driven changes. For example, climate-driven changes in waves impacting Australia's south-west coast might be more affected by SLR modulating the coastal wave field, as opposed to changes in the southern ocean wave field<sup>205</sup>. The implications on the Antarctic coast are unclear owing to the complexity of interactions but wave-induced flexure of the outermost ice shelf regions has been deemed a factor in ice sheet disintegration events along the Antarctic coast over the 2010s<sup>230</sup>.

## Summary and future perspectives

The climatological variability and change in wind-wave characteristics (see summary of key features in Table 1) have increasingly gained attention in recent years, with recognition of the potential impacts such changes can have on coastal systems, and design requirements for coastal and offshore infrastructure. These impacts could exacerbate, and in some instances exceed, the impacts of sea-level rise (SLR). There are several regions of the global oceans where these changes, and their consequent impacts, are already experienced. However, monitoring of wave climate change is limited by available observation systems. Historical change assessments to date are primarily based on satellite altimeter data (limited to estimates of significant wave height, and statistics affected by undersampling issues), in-situ buoys (sparsely distributed, and incomplete records of technology changes through the record have hampered trend investigations), and visual observations (limited accuracy and sampling and observational biases).

Wave reanalysis and hindcast products are often used as observation proxies due to the spatial and temporal scarcity of observations, but they suffer from temporal inhomogeneities as a result of the changes in quantity and quality of ingested observations, which can particularly affect trends. Despite these challenges, there is a general agreement of a consistent historical increase in mean wave heights over the Southern Hemisphere. There is also evidence of atmospheric teleconnection patterns having a strong influence on wind-wave variability. Future wave climate projection studies have primarily focused on mid (RCP4.5) and high (RCP8.5) emission scenarios on ice-free areas, showing statistically significant increases in the mean wave heights over the eastern tropical South Pacific and the Southern Ocean, and decreases over the North Hemisphere. Differences between 1.5°C and 2°C worlds reveal potential benefits of limiting global warming over large regions of global ocean. However, there is a large uncertainty among different climate and wave modelling approaches which particularly affect extremes for which studies show inconclusive results. Moreover, there is limited knowledge of how the ocean wave climate variability, and the interaction of waves with other marine and atmospheric drivers (sea ice, storm surge, sea level rise, coastal morphology change, surface winds, etc.) might affect wave climate change estimates. Limited studies of the Arctic Ocean show outstanding changes there due to sea ice decline but this needs to be further assessed with larger ensembles with improved climate forcing and better sea ice parameterizations. With the recognition of the present challenges, we discuss priorities for future research.

## Sustained increase of observations

The emerging availability of new satellite sensors able to resolve a more complete picture of the wave field (such as SAR missions and CFOSAT SWIM sensors<sup>43,70</sup>, which provide directional wave information), low-cost buoy sensors, and increasingly open access to previously private data holdings will provide greater opportunity to monitor wave field changes. For example, the SOFAR spotter network exceeded 600 buoys in March 2022 and continues to expand rapidly providing a rapid increase in global coverage of wave measurements<sup>260</sup>. However, it is equally important to invest resources in sustaining current observation networks<sup>261</sup>, particularly in-situ moored buoys, with transition to include directional capabilities, and integration into an open-access global systems with consistent accuracy and quality control procedures across platforms<sup>70,261</sup>. Long records provide unique resources to study wave climate variability and trends, and more observations with comprehensive metadata records<sup>70</sup> can also have a positive impact on the homogeneity of derived wave data products (with the help of advanced calibration and homogenization techniques<sup>262</sup>). In addition, VOS records (which date back to the mid-nineteenth century)
offer unique data that should be further used and validated—despite the subjective error and inhomogeneous sampling, VOS
measurements are temporally consistent as operational practices have not changed<sup>70</sup>.

Climate and wave model improvement

Regardless of the increase in observations, climate and wave models will continue to be vital tools for understanding the complex spatial-temporal features of historical and future wave climate. However, these models need to be improved in order to reduce the uncertainty of wave simulations associated with methodological factors. First, this improvement comes with reducing the uncertainty associated with surface wind projections, with one relevant aspect being the better representation of TC as this impacts estimations of low-probability extremes needed for infrastructures and coastal flooding management (as it has been seen for storm surge<sup>263</sup>). High-resolution (0.25° or less) global climate models<sup>63</sup> are needed to better capture TC properties. At high latitudes, it is also relevant to improve sea ice models to reduce existing biases and uncertainties in sea ice formation<sup>264,265</sup>. Second, we need to continue our efforts to improve the energy distribution across the wave spectrum<sup>266</sup>, and better understand several key wave interaction processes with sea ice, currents, and winds at the ocean-atmospheric boundary layer<sup>267</sup>, with one hot topic being the better characterization of wave/sea-ice interactions that are currently absent from Earth system models<sup>210</sup>, meaning existing projections could be underestimating sea ice retreat and wave growth in partially sea ice covered areas. A more precise evaluation of the wave spectra is also needed to better characterize maximum wave heights, which is needed to assess possible impacts on freak waves<sup>268</sup>, which are hazardous waves that are unusually larger than the surrounding waves. Overall, there is need for fundamental research with a multidisciplinary approach<sup>261</sup> (for example, the improvement of wave-ice parameterizations should be carried simultaneously with an improvement of ice models<sup>269</sup>). Also, this research needs to go hand in hand with the acquisition of more observations in other to develop better model parameterizations, and improve data assimilations and validation.

Improved understanding of extreme sea states with larger ensembles and better assessment of the uncer-
tainty

Research on historical and future wind-wave climate should account for a better sampling of the internal natural climate variability, and the tail of the distribution to improve the understanding of the inter-decadal variability and reduce the uncertainty associated with 100-year return period events. The impacts of wave climate change will be felt most acutely in response to any changes in the properties of the extreme wave conditions. Therefore, it is the properties of the extremes that are of most interest to offshore and coastal infrastructure planners and operators. Moreover, larger ensembles with low to medium emission scenarios are required to reduce the uncertainty associated with these extreme wave conditions and identify climate change footprints<sup>54</sup>. With the imminent increase in CMIP6-derived wave studies, it also becomes important to carry out a comprehensive assessment of possible differences relative to the previous CMIP phase. The challenge posed by the large computational cost associated with the need for increasingly large wave ensembles can be addressed with the complementary use of machine learning techniques, which have been successfully applied to a large variety of modelling problems, including recent applications of wind-wave prediction<sup>270</sup>. Also, machine learning can potentially be implemented in areas with complex wave interactions such as sea ice-wave interaction, which are not covered by traditional statistical approaches.

Better coverage and improved high-resolution regional projections

While large-scale and global studies can be used to identify potential hotspot areas, they can be misleading if used directly to quantify wave-driven coastal impacts, which typically require a spatial resolution at kilometer scales<sup>70</sup>. Despite the advances made in region-wide local wave downscaling<sup>271-273</sup>, efforts are needed to improve global coverage of regional and coastal assessments (in particular for low-lying and vulnerable populated coastlines), which need to make use of high-resolution downscaled wave projections that were driven from high-resolution forcing variables. Increased forcing resolution is particularly relevant in sheltered coastlines, where local weather patterns can dominate over the climate change signal<sup>143</sup>. However, increased resolution is not enough. The aforementioned need for fundamental wave modelling research becomes more pressing as getting closer to the coasts, where the more complex wave dynamics require the use of coupled wave-circulation models. It is critical to use enhanced coastal bathymetry information that accounts for local features<sup>261,274</sup>, and to improve wave models to better capture relevant shallow processes such as wave breaking, and its interactions with coastal currents, sediment transport, and coastal erosion<sup>275</sup>. For example, the morphological adjustment to changes in offshore wave conditions can have an important impact on the resulting waves nearshore<sup>5</sup>. With the increase of regional wave projections, it would be ideal to integrate this information into an open-data system, such as the worlwide C3S CORDEX Grand Ensemble<sup>276</sup>, to enable a much needed comprehensive quantitative assessment of regional-scale projections, the contribution of their uncertainty factors, and how it compares to global-scale results.
Integrating other marine and atmospheric drivers

Understanding change in waves is just one of many factors to resolve, as we seek to understand climate change impacts on our coasts and marine systems. From long-term sea level rise scenarios to wind-waves, coastal climate drivers across multiple temporal scales need to be considered as well as their interconnections. For example, over half of the coastlines exhibit dependencies between storm surge and wave extremes²⁷⁷ which, together with intense precipitation or snowmelt, are key drivers of compound flooding²⁷⁸. There is a need to develop impact-based approaches that integrate (nonlinear) interactions and dependencies between waves and other marine/atmospheric drivers of the so-called compound events²⁷⁹,²⁸⁰. In addition, much of the attention of historical and future projected changes in wave characteristics has focused on the influence of climate driven changes in forcing atmospheric conditions. There is evidence to suggest that at the coast, these atmospheric forced driven changes will be overwhelmed by the influence that future changes in nearshore and coastal morphology, associated with SLR, reef growth rates and other coastal processes, have on wave characteristics²⁰⁵,²⁸¹. For example, degraded coral reefs (that might result from weakened structure integrity due to acidification) can be more vulnerable to wave driven destruction and no long offer coastal protection from waves, leading to larger waves nearshore that drive greater coastal impacts²⁸¹,²⁸². Resolving these influences at global scale requires a step up in our observational and systems modelling capabilities.
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287. Gutiérrez, J. & et al. *Atlas. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change* [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L.Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K.Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. (Cambridge University Press, 2021).

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288. Tebaldi, C., Arblaster, J. & Knutti, R. Mapping model agreement on future climate projections. *Geophys. Res. Lett.* **38**, DOI: **10.1029/2011GL049863 (2011).**

1318
1319 Acknowledgements

J.M. acknowledges the University of Central Florida (UCF) Pre-eminent program (P3).

1321 Author contributions

M.C.-P. led the writing of the manuscript, conducted the majority of the analyses presented herein, and made Figs. 2-5, Table 1, and supplementary tables and figures. G.D. made Fig. 1. M.C.-P., M.H., G.D., J.M., X.W., N.M., and I.Y. contributed to the general design of the manuscript, including text structure and figure conceptualization. Y.F. contributed to the statistical data analysis. All co-authors (except Y.F.) contributed to the literature review, writing of initial drafts regarding specific sections, and to editing the final draft. In particular, M.C.-P., L.E. and X.W. contributed to the initial version of the Arctic Ocean section, G.D., M.M., X.W., M.C.-P. and J.M. contributed to the initial version of the Atlantic Ocean section, B.K. and P.K. contributed to the initial version of the Indian Ocean section, N.M., J.M., and X.W. contributed to the initial version of the Pacific Ocean section, and I.Y. and M.H. contributed to the initial version of the Southern Ocean section.

1330 Competing interests

The authors declare no competing interests.
1332 Key points

1333

1334

* A growing number of ocean wave studies have been developed since 2010s leading to an increased understanding of the wind wave climate changes under global warming but important uncertainties remain.

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* Historical trend analysis is challenging due to the presence of temporal inhomogeneities in historical products as a result of an increase of the number and type of assimilated data over time.

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* Future wave projections are affected by a chain of uncertainty factors, including variability related to wave and climate models, emission scenarios, and (the poorly known) internal natural variability.

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1340

* Future wave projections reveal robust increases over the Southern Ocean and tropical South Pacific, with the Arctic Ocean experimenting the most dramatic changes.

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* Resolving global warming effects on coastal wind-waves, in addition to other marine drivers, is key to understand the impact on our coasts, but requires a step-up in our observational and model capabilities.

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* Multidisciplinary fundamental modelling research, sustained increase of observations, and larger ensembles are needed to reduce uncertainty in wave climate changes across multiple scales, including contribution to extreme sea-level change.
<table><caption>**Table 1.** Regional summary of most relevant and robust features of the historical and future changes in wind-wave conditions at each major ocean basin.</caption><thead><tr><th>Region</th><th>Climatology</th><th>Historical change</th><th>Response to teleconnections</th><th>Future projections by 2100 (RCP8.5)</th></tr></thead><tbody><tr><td>Atlantic Ocean</td><td>Latitudinal gradient of H<sub>s</sub><br>Large seasonal & inter-annual variability (ExTNA)<br>Larger T<sub>m</sub> in ESA<br>Fetch-limited waves in Med<br>EW θ<sub>m</sub> in ExTA turning WW in TA</td><td>↑↓ H<sub>s</sub> (Decadal 0.5-3 cm/yr; NA)<br>↑ H<sub>s</sub> (After 1990's: 0.5-3 cm/yr; WMed)</td><td>↑ H<sub>s</sub> (NENA) with NAO+, AO+ & SCAND+<br>↑ H<sub>s</sub> (WsTNA) with NAO- & AO-<br>↑ H<sub>s</sub> (Med) with NAO-, EA-<br>↑ H<sub>s</sub> (ENA) with SCAND+, EA+</td><td>↓ H<sub>s</sub> (&lt;10%; NA & Med)<br>↓ T<sub>m</sub> (&lt;5%; NA & Med)<br>⊙θ<sub>m</sub> (&lt;10°; TA & ExTA)</td></tr><tr><td>Pacific Ocean</td><td>Latitudinal gradient of H<sub>s</sub><br>Complex multi-modal waves in TP & dominant swell in ESP<br>EW θ<sub>m</sub> in ExTP, turning EqW (ETP) & Ws (WTP)</td><td>↓ H<sub>s</sub> (&lt; 1 cm/yr; NP, with exception of WNP & California coast)<br>↑ H<sub>s</sub> (0.5-1 cm/yr; SP)</td><td>Strong ENSO influence<br>↑ H<sub>s</sub> (NEP, SWTP) with SOI- (El Niño)<br>↑ H<sub>s</sub> (NEP) with PDO+ and PNA+</td><td>↓ H<sub>s</sub> (&lt;10%, NP, NWTP)<br>↑ T<sub>m</sub> (&lt;5%, EP)<br>⊙θ<sub>m</sub> (5°; 10°; sTP & TP)<br>⊙θ<sub>m</sub> (5°; 10°; ExTP)</td></tr><tr><td>Indian Ocean</td><td>Poleward positive gradient of H<sub>s</sub><br>SO swell affects NIO & SIO<br>Strong influence of monsoon winds (NIO), which reverse direction annually<br>EW θ<sub>m</sub> (ExTI), & Eqw/SW in summer/winter (NIO)</td><td>↑ H<sub>sDJF</sub> (reg. average 0.4 cm/yr; IO)<br>↑ H<sub>sDJF</sub> (reg. average 0.6 cm/yr; IO)<br>↑ H<sub>s</sub> (&gt;1 cm/yr; SIO)</td><td>↑ H<sub>s</sub> (BoB) during summer monoon & El Niño<br>↑ H<sub>s</sub> (SIO) with SAM+</td><td>↑ H<sub>s</sub> (&lt;10%; NIO, WTIO, all seasons except DJF)<br>↑ T<sub>m</sub> (&lt;5%)<br>⊙θ<sub>m</sub> (&lt;5°; WI)</td></tr><tr><td>Arctic Ocean</td><td>Historically limited wave influence in IA (semi-enclosed seas) & strong seasonal variability<br>EA influenced by NA waves with Nw θ<sub>m</sub></td><td>Emergence of swell & ↑ H<sub>s</sub> (1-3 cm/year, IA)<br>↑ H<sub>s</sub> (&lt;10 cm/yr, particularly autumn)<br>Unprecedented H<sub>s</sub> &gt;5 m (BS) in 2015<br>SIC reduction (with unprecedented minimum in 2012) is a key driver</td><td>↑ H<sub>s</sub> (NS, GS) with AO+, NAO+, and SCAND-Weakening of the normally anticyclonic climate (IA) linked to intrusion of NA waves when favored by SIC decline</td><td>Climate change hotspot with virtually ice-free Arctic by 2050<br>↑ H<sub>s</sub> T<sub>m</sub> (&lt;400%), particularly Jul-Nov above 70°N<br>⊙θ<sub>m</sub> (BS)</td></tr><tr><td>Southern Ocean</td><td>Long fetches with sustained year-round intense waves<br>Generation source of swells influencing PO, AO, IO</td><td>↑ H<sub>s</sub> (1-3 cm/yr)</td><td>↑ H<sub>s</sub> & ↑ Swell with SAM+, AAO+</td><td>↑ H<sub>s</sub> (~5%)<br>↑ T<sub>m</sub> (~5%)<br>⊙θ<sub>m</sub> (3°- 5°)</td></tr></tbody></table>

NA, North Atlantic; ExTNA, Extra-tropical North Atlantic; ESA, Eastern South Atlantic; Med, Mediterranean Sea; ExTA, Extra-tropical Atlantic Ocean; WMed, Western Mediterranean Sea; NENA, Northeastern North Atlantic Ocean; WsTNA, Western sub-tropical North Atlantic Ocean; ENA, Eastern North Atlantic; TA, Tropical Atlantic; TP, Tropical Pacific; ESP, Eastern South Pacific; ExTP, Extra-tropical Pacific; ETP, Eastern Tropical Pacific; WTP, Western Tropical Pacific; NP, North Pacific; WNP, Western North Pacific; NEP, Northeastern Pacific; SWTP, Southwestern Tropical Pacific; NWTP, Northwestern Tropical Pacific; EP, Eastern Pacific; sTP, sub-Tropical Pacific; SO; Southern Ocean; NIO, North Indian Ocean; SIO, South Indian Ocean; ExTIO, Extra-tropical Indian Ocean; IO; Indian Ocean; BoB, Bay of Bengal; WTIO, Western Tropical Indian Ocean; WIO: Western Indian Ocean; IA; Inner Arctic; EA, Eastern Arctic; BS, Beaufort Sea; NS, Norwegian Sea; GS, Greenland Sea; PO, Pacific Ocean, AO, Atlantic Ocean; EW, Eastwards; WW, Westwards; EqW, Equator-wards; SW, Southwards; SIC, Sea ice cover; DJF, December-January-February. Unless otherwise stated, historical and projected changes refer to mean climatological values, and trends are specified for the 1980s to 2010s period. H<sub>s</sub> indicates high-frequency H<sub>s</sub> extremes.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Spatial coverage and temporal evolution of *H*<sub>s</sub> observations (a) Spatial sampling of wave buoys (colored circles) and one-day satellite acquisition of altimeter (grey line) and Synthetic aperture radar (SAR) missions (red dotted line). (b) Temporal evolution of the yearly number of significant wave height (*H*<sub>s</sub>) observations from 1970 to 2020, including wave buoys (from the Copernicus Marine Service In Situ Thematic Center, available at</figcaption></figure>

https://marine.copernicus.eu/about/producers/insitu-tac), altimeter and SAR missions (from the
ESA Sea State CCI database collection, available at

https://catalogue.ceda.ac.uk/uuid/7cfcd20428c3454fafa4e1afec2cf92). Buoy sampling rate is comprised between 1-360 min (with over 70% buoys having either 30 or 60 min sampling rate), altimeter sampling rate is 1 Hz (corresponding to ~ 7km spacing), and SAR sampling rate is ~ 15 s (corresponding to ~ 100km spacing). Only buoys with more than 5 years of records are shown. Altimeter missions include ERS-1, TOPEX, ERS-2, GFO, Jason-1, ENVISAT, Jason-2, Cryosat-2, SARAL, Jason-3 and Sentinel-3A. SAR missions include ENVISAT, Sentinel-1A and Sentinel-1B. Note that for the one-day example tracks shown in (a) only Jason-2, Cryosat-2 SARAL, Jason-3, Sentinel-3A, Sentinel-1A and Sentinel-1B are included. This figure illustrates the heterogeneous spatial coverage of moored buoys (with a larger density in the North Hemisphere), the limited time coverage of moored buoys (the large majority of buoys have only been operative for the last 20 years or less while only few buoys (violet) have been operative for more than 40 years), the near-global coverage of satellite acquisitions with a lower time resolution, and the notable increase of yearly number of wave observations over the last decades, with a big jump in the 1990s thanks to the contribution of satellite missions.
<figure><img src="image_3.png" /><figcaption>(b) $H_s$ trends (cm/yr) derived from reanalysis/hindcast members and comparison with ensemble</figcaption></figure>

<figure><img src="image_4.png" /></figure>

**Figure 2. Historical $H_s$ trend and discrepancies among data products.** Annual mean significant wave height ($H_s$) trend (cm/yr) calculated over the indicated periods from (a) altimetry data (in comparison to reanalysis/hindcast ensemble average), and (b) individual ensemble members (in comparison with corresponding ensemble with and without CFSR-derived products). Results are derived from the IMOS global merged multi-mission monthly gridded altimetry dataset<sup>283,284</sup>, the ESA CCI L4 product v1.1<sup>285</sup>, and a global ensemble of ocean wave climate statistics from contemporary wave reanalysis and hindcasts<sup>31</sup> (see Table S1). The trend is computed with Sen's slope estimator in conjunction with a modified Mann-Kendall method that accounts for the effect of lag-1 autocorrelation by iterative pre-whitening<sup>55,286</sup>. Stippling indicates statistical significance of trends derived from individual products. Robustness and uncertainty in the ensemble averages is displayed as in the IPCC AR6 Interactive Atlas<sup>287</sup> with robust signal (no hatching) being defined as > 50% models show statistically significant trend and 80% of those models agree on sign of change<sup>288</sup>. The ensemble average is weighted average so each driving atmospheric model has equal contribution. This figure illustrates the challenge in assessing trends due to the discrepancies among modern wave reanalyses/hindcasts and altimetry data, which relates to the presence of temporal inhomogeneities caused by the increase of observations overtime, and calibration differences.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Historical climatology and variability of wind-waves. (a) Ensemble average of the historical climatological mean of the annual mean significant wave height ($H_s$) (m) (left panel), the ensemble average of its inter-annual variability (centre panel), and the corresponding inter-member variability (right panel). (b) As in panel (a) but annual maximum $H_s$ (m). (c) As in panel (a) but annual mean $T_m$ (s). (d) As in panel (a) but annual mean $\theta_m$ (°, nautical convention). Results are derived from a global ensemble of ocean wave climate statistics from contemporary wave reanalysis and hindcasts³¹ that covers 1980–2014, with the exception of one ensemble member that covers 1980–2012 (see Table S1). CFSR-IFREMER $T_m$ was not considered due the different $T_m$ formulation (see Figure S4). The ensemble average is weighted average so each driving atmospheric model has equal contribution. The inter-annual variability is described as the ensemble average of the standard deviation of the corresponding annual values. The inter-member variability is described as the standard deviation of the corresponding climatological means of all members. This figure illustrates large-scale wind-wave features, such as energetic sea states in the mid-to-high latitudes and swell-dominated long waves in the Southern Ocean and the Eastern side of large basins, while it highlights regional uncertainty due to inter-member variability.</figcaption></figure>
<figure><img src="image_6.png" /></figure>

**Figure 4.** Areas of increased *H*<sub>s</sub> during positive or negative phase of the indicated teleconnection pattern. Results are derived from a global ensemble of ocean wave climate statistics from contemporary wave reanalysis and hindcasts<sup>31</sup> that covers 1980–2014, with the exception of one ensemble member that covers 1980–2012 (see Figs. S12-S13 and Table S1). It also considers the North Atlantic Oscillation (NAO) index, the Arctic Oscillation (AO) index, the East Atlantic (EA) index, the Scandinavian (SCAND) index, the Southern Oscillation Index (SOI), the Pacific Decadal Oscillation (PDF) index, the Pacific North American (PNA) index, the Southern Annular Mode (SAM) Index, and the Antarctic Oscillation (AAO) index. Sustained large negative values of the SOI indicate an El Niño, positive values indicate (La Niña). The periods of positive (negative) phase are defined as the months when the corresponding teleconnection pattern standardized index is positive (negative) and exceeds one standard deviation in absolute value. Areas of increased wave height are identified where 80% of the ensemble members exhibit an averaged monthly mean *H*<sub>s</sub> over the months of, respectively, positive and negative phases of the corresponding teleconnection pattern, that is at least 5% larger than the average of the climatological monthly mean *H*<sub>s</sub> values. This figure illustrates large-scale atmospheric teleconnection patterns have an influence on wind-waves.
<figure><img src="image_7.png" /><figcaption>(b) North Atlantic (NA)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) Eastern Tropical South Pacific (ETSP)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) Southern Ocean (SO)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(e) Arctic Ocean (AO)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(f) Global oceans (excluding the partially sea-ice covered areas)</figcaption></figure>

<figure><img src="image_12.png" /></figure>

**Figure 5.** Future projected changes in $H_s$. (a) The ensemble average of the future (2081-2099) projected change of the climatological mean of the annual mean significant wave height ($H_s$) (m) for the RCP8.5 scenario, relative to the climatological mean of the historical period (1979-2004). Robustness and uncertainty is displayed as in the IPCC AR6 Interactive Atlas<sup>287</sup> with robust signal being defined as > 50% models show statistically significant change and 80% of these models agree on sign of change<sup>288</sup>. (b-f) Evolution of the regional average (over the indicated areas) of the yearly annual mean $H_s$ (m) relative to the corresponding climatological mean of the historical period (1979-2004) (%), including RCP4.5 and RCP8.5 scenarios. Results (except for the Arctic Ocean) are derived from the latest global ensemble of ocean wave climate projections from CMIP5-driven models<sup>36</sup>. Results relative to the Arctic Ocean are derived from CMIP5-driven 5-member ensemble<sup>95</sup>. For each year in the regional panels (b-f), the inter-member variability is described as the standard deviation of the corresponding relative projected change for all members of the historical period (black), RCP4.5 scenario (blue), RCP8.5 scenario (red). This figure illustrates global $H_s$ has no clear sign of increase or decrease but some regions exhibit a decrease or increase up to 10% (larger for RCP8.5 than for RCP4.5), except for the Arctic Ocean where relative changes are remarkably larger (note the change in scale).
**Box 1** | Description of wind-waves

Wind-waves are only one type amongst a variety of waves that occur in the oceans, being typically shorter than 30 s and longer than 1/4 s². As with many other types of waves, they can generally be described by their wave height (H), wave period (T), and wave direction (θ). However, the definition of wave height, or wave period, is non-trivial as the sea state typically results from the combination of many harmonic wave components with different amplitudes, periods (or frequencies, f), phases and directions, that can be described by a 3D variance density wave spectrum² (E(f, θ)), which can be simplified by a 2D spectrum by integrating over all directions (E(f)). For practical purposes, we often use spectrum-averaged (or derived) wave parameters to describe wind waves, being the most commonly used the significant wave height Hs, the mean(peak) wave period Tm (Tp) and the mean(peak) wave direction θm (θp).

Hs is a well-defined and standardized statistic to describe the characteristic wave height of the sea state, which is defined as the average height of the highest one-third of waves. It is largely used in coastal, naval, and offshore engineering, being one of the reasons for its widespread use the fact that Hs correlates fairly well with the wave height as historically estimated by experienced observers². Tm, Tp, θm, and θp are also relevant spectrum-derived wave statistics that are widely used by researchers and engineers. Tm and θm are obtained from integrating the spectrum, while Tp and θp focus on the predominant (most energetic) wave system. These wave parameters are relevant metrics that have been, and continue to be, used to monitor changes in wave conditions, and assess their impacts. For example, high and steep waves (large Hs/L, where L is the wavelength and a function of Tm) have a larger potential for beach erosion, and infrastructure damage²², while swell-dominated sea states with large wave periods are a flooding hazard for low-lying coastal areas²⁴⁶. Tm is also relevant for coastal and naval engineering as it can be linked to wave resonance and associated instability, while the combination of wave period and wave height (Hs²Tp) translates into wave power. θm is a key feature affecting the long-shore sediment transport along coastal beaches, which can contribute to long-term coastal retreat. With increased accessibility to technology (storage and compute) and ability to analyse large and complex data, researchers are increasingly assessing characteristics of the full wave spectra over global scales.
2D

<figure><img src="image_13.png" /></figure>

3D

<figure><img src="image_14.png" /></figure>