140 Years of Global Ocean Wind-Wave Climate Derived from CMIP6 ACCESS-CM2 and EC-Earth3 GCMs: Global Trends, Regional Changes, and Future Projections

Alberto Meucci aDepartment of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia

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Ian R. Young aDepartment of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, Australia

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Mark Hemer bCSIRO Oceans and Atmosphere, Hobart, Tasmania, Australia

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Claire Trenham cCSIRO Oceans and Atmosphere, Canberra, Australian Capital Territory, Australia

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Ian G. Watterson dCSIRO Climate Science Centre, Aspendale, Victoria, Australia

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Abstract

We present four 140-yr wind-wave climate simulations (1961–2100) forced with surface wind speed and sea ice concentration from two CMIP6 GCMs under two different climate scenarios: SSP1–2.6 and SSP5–8.5. A global three-grid system is implemented in WAVEWATCH III to simulate the wave–ice interactions in the Arctic and Antarctic regions. The models perform well in comparison with global satellite altimeter and in situ buoys climatology. The comparison with traditional trend analyses demonstrates the present GCM-forced wave models’ ability to reproduce the main historical climate signals. The long-term datasets allow a comprehensive description of the twentieth- and twenty-first-century wave climate and yield statistically robust trends. Analysis of the latest IPCC ocean climatic regions highlights four regions where changes in wave climate are projected to be most significant: the Arctic, the North Pacific, the North Atlantic, and the Southern Ocean. The main driver of offshore wave climate change is the wind, except for the Arctic where the significant sea ice retreat causes a sharp increase in the projected wave heights. Distinct changes in the wave period and the wave direction are found in the Southern Hemisphere, where the poleward shift of the Southern Ocean westerlies causes an increase in the wave period of up to 5% and a counterclockwise change in wave direction of up to 5°. The new CMIP6 forced wave models improve in performance compared to previous CMIP5 forced wave models, and will ultimately contribute to a new CMIP6 wind-wave climate model ensemble, crucial for coastal adaptation strategies and the design of future marine offshore structures and operations.

Significance Statement

The purpose of this study is to advance the understanding of ocean wind-wave climate evolution over the twentieth and twenty-first centuries and to effectively communicate the long-term impacts of climate change in diverse wind-wave climatic regions across the globe. The 140-yr continuous model results produced in this work are crucial to studying changes in extreme sea states and investigating the relationship between interdecadal periodic oscillations and long-term climate trends. The dataset produced can be used to gain further insight into the substantial long-term changes of the polar wind-wave climate caused by the rapid decrease of sea ice coverage, and the evolution of the directional changes in the sea states triggered by climate change.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alberto Meucci, alberto.meucci@unimelb.edu.au

Abstract

We present four 140-yr wind-wave climate simulations (1961–2100) forced with surface wind speed and sea ice concentration from two CMIP6 GCMs under two different climate scenarios: SSP1–2.6 and SSP5–8.5. A global three-grid system is implemented in WAVEWATCH III to simulate the wave–ice interactions in the Arctic and Antarctic regions. The models perform well in comparison with global satellite altimeter and in situ buoys climatology. The comparison with traditional trend analyses demonstrates the present GCM-forced wave models’ ability to reproduce the main historical climate signals. The long-term datasets allow a comprehensive description of the twentieth- and twenty-first-century wave climate and yield statistically robust trends. Analysis of the latest IPCC ocean climatic regions highlights four regions where changes in wave climate are projected to be most significant: the Arctic, the North Pacific, the North Atlantic, and the Southern Ocean. The main driver of offshore wave climate change is the wind, except for the Arctic where the significant sea ice retreat causes a sharp increase in the projected wave heights. Distinct changes in the wave period and the wave direction are found in the Southern Hemisphere, where the poleward shift of the Southern Ocean westerlies causes an increase in the wave period of up to 5% and a counterclockwise change in wave direction of up to 5°. The new CMIP6 forced wave models improve in performance compared to previous CMIP5 forced wave models, and will ultimately contribute to a new CMIP6 wind-wave climate model ensemble, crucial for coastal adaptation strategies and the design of future marine offshore structures and operations.

Significance Statement

The purpose of this study is to advance the understanding of ocean wind-wave climate evolution over the twentieth and twenty-first centuries and to effectively communicate the long-term impacts of climate change in diverse wind-wave climatic regions across the globe. The 140-yr continuous model results produced in this work are crucial to studying changes in extreme sea states and investigating the relationship between interdecadal periodic oscillations and long-term climate trends. The dataset produced can be used to gain further insight into the substantial long-term changes of the polar wind-wave climate caused by the rapid decrease of sea ice coverage, and the evolution of the directional changes in the sea states triggered by climate change.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alberto Meucci, alberto.meucci@unimelb.edu.au

1. Introduction

Observing, predicting, and analyzing ocean wind-waves—surface gravity waves generated by the action of the wind over the ocean surface—has always been of major interest for practical engineering purposes (Holthuijsen 2010). Wind-waves not only affect human activities at sea but also the safety of coastal communities (Hemer et al. 2012; Mentaschi et al. 2017; Marcos et al. 2019; Kirezci et al. 2020; Melet et al. 2020; Hinkel et al. 2021). On longer time scales, the wind-wave climate shapes coastal ecosystems, and singular and compound extreme events may result in significant loss of life (Lowe et al. 2010; Collins et al. 2019).

Similar to other Earth climate system processes, wind-waves are affected by human-induced climate change (Hemer et al. 2013; Morim et al. 2019; Meucci et al. 2020b). Studies have shown that the global wind-wave climate has experienced statistically significant changes over the past 30 years (Young et al. 2011; Young and Ribal 2019; Timmermans et al. 2020). These changes are projected to continue in the twenty-first century (Hemer et al. 2013; Morim et al. 2019; Meucci et al. 2020b). In the delicate and variable context of a fast changing climate (Meehl et al. 2020), it is crucial to understand how the wind-wave climate is evolving. The expanding marine economy (Sardain et al. 2019; Bugnot et al. 2021) and the increasing population living on the coastlines (Hinkel et al. 2014) call for accurate and easy to interpret long-term continuous wind-wave climate projections. An accurate assessment of future projected wave climate changes is crucial to reduce the uncertainties of future coastal flood risk studies and ultimately support coastal climate adaptation strategies (Hinkel et al. 2021).

The first critical step in understanding projected changes in future global wave climate is to investigate the historical wind-wave climate and its long-term changes. Studies to date have used different approaches and datasets. Each of them provides valuable insight but with limitations. Gulev and Grigorieva (2004, 2006) studied the past ocean wind-wave climate from a large dataset of voluntary ship observations but, even with the latest updated dataset extending back to the nineteenth century (Grigorieva et al. 2017), the sparsity in time and space of observations hinders accurate wind-wave climate trend estimates. Because of such in situ data limitations, global wind-wave climate analyses from satellite observations are more common. Observations from different satellite missions have been collected and calibrated to form comprehensive datasets (Ribal and Young 2019; Dodet et al. 2020). These are compelling datasets to evaluate surface wind speed and significant wave height climate trends (Young and Ribal 2019). However, the actual magnitude of these trends is questionable as it depends on different calibration approaches and mission choices (Timmermans et al. 2020; Young and Ribal 2022).

To complement climate analysis from the observational datasets and overcome some of the limitations, an extensive number of studies have focused on analyzing the past wind-wave climate and its changes through the use of hindcasts, reanalyses or dynamically downscaled global circulation models (GCMs). These are three distinct products with different characteristics. Hindcasts and reanalyses are particularly accurate in reproducing wind-wave average climate variability. However, the inhomogeneities caused by the different number and quality of assimilated observations may lead to spurious trends (Wohland et al. 2019; Meucci et al. 2020a; Timmermans et al. 2020).

GCMs are constrained only by a few boundary conditions and implement our present understanding of the coupled ocean–atmosphere system to simulate the evolution of the climate in time and space. The advantage of using dynamically downscaled GCMs is that we can test the viability of the product in the historical climate, to then use it to project the future wind-wave climate. No observations are assimilated in GCMs which means that no discontinuities are found in the GCMs’ data series but appropriate analysis is needed to understand if such models are correctly representing the historical climate. Dynamical or statistical downscaling approaches based on GCMs have been largely implemented to study the wind-wave climate changes. These products are characterized by numerous sources of uncertainty (Morim et al. 2018), and multimodel ensemble analyses are performed to increase the confidence in the climate estimates (Morim et al. 2019; Meucci et al. 2020b).

The reference international wind-wave climate ensemble (Morim et al. 2020b) is a collection of dynamically and statistically downscaled wave datasets from previous Coupled Model Intercomparison Project phases, CMIP3 and CMIP5. As part of the CMIP6 coordinated effort (Eyring et al. 2016) international institutions produced new coupled ocean–atmosphere GCMs, with increased resolution and improved physics (Mauritsen et al. 2019; Bi et al. 2020; Boucher et al. 2020; Döscher et al. 2022; Pak et al. 2021). When compared to previous CMIP phases’ GCMs, CMIP6 GCMs show improved representation of atmospheric processes. In particular, the reduced biases in simulating extratropical cyclone intensity both in the Northern and the Southern Hemisphere (Priestley et al. 2020; Harvey et al. 2020), and a better simulation of the frequency and spatial distribution of cut-off lows (Pinheiro et al. 2022), are crucial for better GCM-forced wind-wave model simulations. Furthermore, a new future scenario framework was introduced with the new Shared Socioeconomic Pathways (SSPs), which integrate socioeconomic developments into future climate scenarios (Riahi et al. 2017).

Considering the improved GCMs’ representation of Earth’s climate and the integrated approach to future scenarios, it makes sense that GCM-forced ocean wave climate models are updated to the latest CMIP phase. A computationally efficient option to update wind-wave climate datasets is to continue with traditional time slices simulations, to then compare historical and future projection time slices and estimate future projected changes (Hemer et al. 2013; Mentaschi et al. 2017; Morim et al. 2019; Meucci et al. 2020a; Casas-Prat and Wang 2020; Amores and Marcos 2020). However, the ocean wave climate is modulated by climate variability (Hemer et al. 2010; Stopa and Cheung 2014; Kumar et al. 2016) and, as such, it is important to assess the impact of these oscillations on wind-wave climate change studies. To do so, we need long-term continuous datasets that describe the evolution of the climate across several decades (Song et al. 2020).

Within this context, this work presents an extensive and in-depth analysis of 140 years (1961–2100) simulated global wind-wave climate forced by the surface wind speed and sea ice concentration of two new CMIP6 GCMs (Bi et al. 2020; Döscher et al. 2022). The datasets produced update the current state-of-the-art wave climate datasets with the newly improved CMIP6 GCMs forcing, and two long-term continuous multiscenario dataset to analyze the impact of climate variability on future ocean surface wave projections. As the GCMs’ representation of surface winds and sea ice concentrations may substantially differ in specific regions, a future ensemble of CMIP6 GCM-forced models is needed. As such, we propose a computationally efficient state-of-the-art model framework propaedeutic to the production of an eight-model ensemble of CMIP6 GCM-forced wind-wave climate models. The present project is set within the context of an international effort in upgrading and ameliorating wind-wave climate simulations. The project final objective is to contribute to a new international ensemble of newly upgraded CMIP6 wind-wave climate models, in continuation of the effort of the COWCLIP community (Hemer et al. 2012; Morim et al. 2020b).

This paper is organized as follows. In section 2 we describe the wind-wave climate simulations performed, the physics of the model, the numerical implementation, outputs we extracted for analysis, and finally the wind stress calibration performed on the wave model. Section 3 presents the historical wind-wave climate statistics from the two GCMs climate runs evaluated against benchmark observations, with an in-depth analysis of the peak wave period climate with consideration of modeled directional spectra. Additional evaluation against ERA5 and a 40-yr global hindcast, with similar wave model settings, is shown in the supplemental material. In section 4 we compare our models with a CMIP6 long-term continuous wind-wave climate dataset, the FIO-ESM v2.0 (Song et al. 2020), and an ensemble of wind-wave simulations forced with previous CMIP versions of the GCMs used in this project. In section 5 we evaluate the performance of the present CMIP6 wind-wave climate runs historical trends with reference satellite altimeter and reanalysis datasets and illustrate the results of the 140-yr long-term trend analysis of the wave climate runs. In section 6 we present the future projected wind-wave climate anomalies averaged over the recently updated Intergovernmental Panel on Climate Change (IPCC) climatic regions (Iturbide et al. 2020). Section 7 describes time slice future projection changes for the main wind-wave model outputs.

2. Global wave climate models

To model the global wave climate, we use the third-generation wave model, WAVEWATCH III v6.07, hereafter WW3 [The WAVEWATCH III Development Group (WW3DG) 2019], with wind and sea ice concentration inputs from two different CMIP6 GCMs. The wave model developed for this study simulates the wind-wave data with the latest wave model physics source terms (Rogers et al. 2012; Zieger et al. 2015; Liu et al. 2019), based on an extensive experimental background (Donelan et al. 2005, 2006; Young and Babanin 2006; Babanin et al. 2007; Young et al. 2013). Details about the physics and numerical implementation can be found in the supplemental material.

Coupling with the atmosphere and the ocean is beyond the scope of this work. The impact of dynamically coupling a wave model to a GCM has not yet been explored extensively. An example of a coupled approach to wind-wave climate models can be found in Song et al. (2020) (see Fig. 10i). However, the added value for climate statistics is still not clear as a comprehensive ensemble of wave coupled GCMs is not yet available. In this section, we present the global wave climate runs performed, and the skill score analysis to select the GCMs wind and sea ice forcing. As global wave models need to be calibrated to the input wind field (Stopa 2018), we also present an assessment of the impact of wind stress calibration on the wave climate.

a. Wind-wave climate runs

The objective of the present study is to update the state-of-the-art of global wind-wave climate analyses by introducing two 140-yr WW3/CMIP6 long-term continuous wind-wave climate simulations. The long duration continuous datasets allow the analysis of the wind-wave climate evolution across the CMIP6 historical, 1961–2014, and the future, 2015–2100, GCM simulations. In addition to this, given the importance of the Arctic and Antarctic wave climate for practical applications we model the polar sea ice regions through the use of a two-way interacting three-grid system (Rogers and Linzell 2018). To do so, we used two CMIP6 GCMs: The Australian ACCESS-CM2 (Bi et al. 2020), and the European EC-Earth3 (Döscher et al. 2022) GCMs, hereafter ACM2 and EC3. These models were selected because both provide 3-hourly eastward and northward components of the 10-m surface wind and daily averages of sea ice concentration around the poles, and both perform well in reproducing climate metrics (see section 2b).

Table 1 summarizes the characteristics of the wind and sea ice input used. The wind speed horizontal resolution at the midlatitudes is ≈135 km for ACM2 and ≈80 km for EC3. The WW3 wave model is forced with the r1i1p1f1 (r: Realization, i: Initialization, p: Physics, f: Forcing) ensemble member of each GCM. We simulate the wind-wave climate future conditions under two Shared Socioeconomic Pathways, SSP1–2.6 and SSP5–8.5 (O’Neill et al. 2016; Riahi et al. 2017). The ACM2 and EC3 wind and sea ice inputs are bilinearly regridded from their native grid to a 1° × 1° regular grid to use them as input for the WW3 model. This choice was made in view of consistency and storage constraints for the production of a planned eight-model ensemble of CMIP6-forced wave climate simulations. The resolution of EC3 is slightly better than 1° but its adequacy in reproducing tropical cyclone wind fields remains limited (Timmermans et al. 2017). As such, we judge the loss in extreme sea state performance for the WW3/EC3 simulation as minimal.

Table 1

Wind and sea ice GCM input characteristics.

Table 1

We selected SSP1–2.6 as it is the scenario that closely relates to the Paris Agreement international treaty which aims at limiting global warming to preferably less than 1.5°C compared to preindustrial levels. At the other extreme, we selected SSP5–8.5 as the benchmark high-end emission scenario and in continuity with the CMIP5 RCP8.5 scenario used in previous studies (Morim et al. 2019; Meucci et al. 2020b). Note that the SSP5–8.5 scenario is no longer considered as a probable future (Hausfather and Peters 2020) but it is still useful as reference for future wind-wave climate variability.

Table 2 summarizes the different simulations run with WW3. Throughout the paper, we will refer to these two dynamically downscaled wave climate models as WW3/ACM2 and WW3/EC3.

Table 2

Wind-wave climate model 140-yr long-term runs.

Table 2

b. Skill score analysis for GCMs selection

A new assessment of the climatological skill of the historical simulations from the full CMIP6 ensemble was performed in order to identify two of the best performing GCMs for the present application. We found these to be ACM2 and EC3. The approach follows several previous assessments including that of CMIP5 models by Watterson (2015). The seasonal climatologies of four wind-related variables are compared with those from the fifth version of the ECMWF reanalysis (ERA5) (Hersbach et al. 2020). Liu et al. (2021) compared the ERA5 10-m wind speed, 10-m neutral wind speed, and the CFSR wind speed against the Ribal and Young (2019) satellite altimeter measurements. The comparison shows a slightly stronger negative bias of the ERA5 winds, but an overall better global RMSE in comparison with the CFSR wind speed. Thus, we opted to compare the GCMs near-surface (10 -m) winds with ERA5.

Using the same historical simulation period (1985–2014), monthly mean data for the near-surface (10 m) winds, U10 (sfcWind, in the CMIP6 nomenclature), are available from ACM2, EC3 and a further 40 GCMs. We assess the mean wind speed (sfcWind), the northward (uas) and eastward (vas) components of the 10-m winds, and also the sea level pressure (psl). Seasonal climatologies for 1985–2014 are formed for all these data and for the corresponding quantities from ERA5. The focus here is on the nondimensional M score (Hemer and Trenham 2016), as values for different variables can be averaged, and typically there is a similar range of values from each. For the model field X and observed field Y over a domain, the M score used here is given in Eq. (1):
M=2π×arcsin[1mseVX+VY+(GXGY)2]×1000,
where mse is the mean square error between X and Y, and V and G are the spatial variance and mean of the fields (as subscripted), respectively. Naturally, the grid squares are weighted by area in these calculations. Both X and Y are remapped to the 1° grid used for inputs to the ACM2 and EC3 forced wave model. Since ERA5 is on a 0.25° grid, a conservative method was used for it. This is an area-weighted regridding approach that computes each target grid box as a weighted mean of all source grid boxes (Python Scipy ‘Iris’ tool). A linear interpolation was used for the GCMs. Here the domain is the global ocean, excluding the polar caps (grid points at 75° and poleward). With this formulation, an M score of 1000 occurs only for X = Y, that is, the model is the same as the observations. Positive values mean some skill, decreasing to “no skill”, for 0 or negative values. To provide an overall skill score for each variable, the M scores for each of the four standard seasons are averaged. These are given in Table 3, along with the average over the scores for the four variables, Ave-4. This is used to rank the GCMs in descending order of Ave-4. Based on Ave-4 the top ranked model is EC-Earth3-Veg, with only slightly lower scores for EC-Earth3 and the other variants. Since these historical simulations feature internally generated year-to-year variability, there is some statistical variation in scores, although this is typically small for a global domain. Under this assessment, for overall wind-related skill, EC3 is ranked 2nd out of the available 42 CMIP6 GCMs, and ACM2 is ranked 15th. The ranks for the individual variables are similar (3–6 for EC3, 10–17 for ACM2), demonstrating that these variables are interrelated. It is useful to note that the all-season mean wind speed averaged over the domain from ERA5 is 7.34 m s−1. The 42 GCMs yield a mean overall wind speed of 7.40 m s−1, with a range of 1.5 m s−1 (Table S1 in the online supplemental material). The agreement with ERA5 for mean wind speed is encouraging and supports the use of ERA5 as a validation source. The selected GCMs rank highly in Table 1 and are close to ERA5 in terms of mean wind speed, 7.26 m s−1 for EC3 and 7.54 m s−1 for ACM2.
Table 3

The four-season average M score for each of the four wind-related variables, from the available CMIP6 models. The average of the four is Ave-4, which provides the rank order. The boldface models are the wave model forcing chosen in the present work.

Table 3

Very few satellite observations are available in the Ribal and Young (2019) dataset in the sea ice regions, and large uncertainties characterize benchmark models such as ERA5. Despite that, we perform a skill-score analysis to assess the sea ice representation performance of 38 GCMs similar to the one performed for the wind speed (Table S1). At the North Pole, EC3 ranks 22nd and ACM2 ranks 27th. At the South Pole, ACM2 ranks 13th and EC3 ranks 29th. An extended analysis for the Antarctic region is found in Roach et al. (2020). The comparison between ACM2 and EC3 sea ice concentrations shows similar Arctic sea ice concentrations. Consistent with Roach et al. (2020) we found that the ACM2 and EC3 Antarctic sea ice concentrations are significantly different. When compared against sea ice observational records, the ACM2 sea ice performs reasonably well in the Southern Hemisphere winter but is biased low in the summer, whereas EC3 is biased low both in winter and summer (Roach et al. 2020). Further studies are needed to understand if the GCMs representation of Antarctic sea ice has an influence on the wave climate of the Southern Hemisphere.

c. Wind stress calibration

Spectral wave models typically have a number of tuning parameters that help to calibrate the model results to the best available observations. An advantage of using the new WW3 ST6 physics package is that the physical parameterization is observation-based (Babanin et al. 2001; Donelan et al. 2005; Young et al. 2005; Young and Babanin 2006). Nonetheless, a small amount of tuning is still involved. In the present model configuration, we use the Liu et al. (2019) recalibrated ST6 default parameters. The only calibration implemented in the present climate models concerns the wind friction velocity, or wind stress, u. Such calibration is crucial given the uncertainties in the climate model representation of surface wind speeds (McInnes et al. 2011; Morim et al. 2020a).

The wind friction velocity is proportional to the 10-m surface wind speed U10 through the wind drag coefficient Cd. In the present model setup, u is derived from U10 through the Hwang (2011) empirical formulation, later capped for strong winds by Rogers et al. (2012). In WW3, Cd is multiplied by a calibration value, Cd × FAC (= CDFAC). The CDFAC parameter can be set to adjust the wind stress resulting from different wind forcing.

We test two CDFAC values, 1.0 and 1.08, and run two full 140-yr simulations. The first CDFAC value follows the original ST6 calibration performed by Zieger et al. (2015) based on CFSR reanalysis winds (Saha et al. 2010). The second CDFAC value of 1.08 originates from the calibration performed by Liu et al. (2021) based on global satellite altimeter observed wind speeds. The two 140-yr runs are compared to understand the impacts of such calibration on the historical climate, and the future projected changes.

Figure 1 shows the differences in the significant wave height, Hs, 1985–2014 climate for the WW3/ACM2 (Figs. 1a–c), and the WW3/EC3 (Figs. 1d–f). Note that this time period was selected as it corresponds to the duration of the altimeter data of Ribal and Young (2019). The global differences are computed by subtracting the CDFAC1.0 climate results from the CDFAC1.08 results (CDFAC1.08 − CDFAC1.0). Results are shown for mean, 90th- and 99th-percentile values of Hs. The percentiles are computed using the full 30-yr time series with no averaging involved. The impact of the calibration is higher at the extremes, reaching a difference in the 30-yr Hs average of up to 60 cm for the WW3/EC3 99th percentile Hs (Fig. 1f). The spatial distribution shows that the largest impact of the calibration is found at the high latitudes where the winds are generally stronger. The Southern Ocean region is the most sensitive to the CDFAC calibration, showing the highest discrepancies in the region below the Indian Ocean with up to 30-cm difference in the 30-yr Hs average climate.

Fig. 1.
Fig. 1.

The impact of the ST6 wind stress parameter calibration (CDFAC) on Hs. (a)–(f) Difference in Hs (over the period 1985–2014) between CDFAC = 1.08 and CDFAC = 1.00 for (a),(d) mean Hs, (b),(e) 90th-percentile Hs and (c),(f) 99th-percentile Hs. (g)–(i) Impact of different values of CDFAC on future projections of Hs (ΔHsCDFAC=1.08ΔHsCDFAC=1.0).

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

We also evaluate the impact of the wind stress calibration on the future projected changes in the wind-wave climate (Figs. 1g–i). To do so, we compute the differences in the significant wave height, ΔHs, for the mean, 90th and 99th percentiles between two 30-yr time slices: the historical period, 1985–2014, and the future projected SSP5–8.5 scenario at the end of the twenty-first century, 2071–2100. The calibration is tested for the WW3/ACM2 model, as the WW3/EC3 historical calibration showed similar results, and to reduce computational expense. The ΔHs difference is calculated as ΔHsCDFAC=1.08ΔHsCDFAC=1.0. Figures 1g–i show that the impact of the calibration on the Hs future projected changes is mostly felt at the extremes, especially at the 99th percentile. Overall, the calibration has a small impact on the results with a maximum of ∼5 cm difference for the 99th-percentile calibration test. This result shows that, within the CDFAC values chosen (i.e., 1.00 and 1.08), the projected changes in global wave climate are largely insensitive to the model calibration.

After comparing the WW3/ACM2 and WW3/EC3 historical climate results with satellite altimeter and buoy observations, as well as the ERA5 dataset (Hersbach et al. 2020), we opted to run both WW3/ACM2 and WW3/EC3 models with the default CDFAC of 1.0.

d. Model output

The WW3/ACM2 and WW3/EC3 field outputs are extracted every 3 h and interpolated over a 0.5° global regular grid from 90°N to 90°S (Meucci et al. 2021). The integral parameters extracted are the significant wave height Hs, the 10-m surface wind speed U10, the peak frequency fp from which we derive the peak period as Tp = 1/fp, the mean wave direction θ¯, the peak wave direction, θp, the second-order mean wave period Tm,02, three Hs partitions, as derived from the default topographic spectral partitioning of WW3 (wind-sea pHs,0, primary swell pHs,1, secondary swell, pHs,2), the wave energy flux cge. In addition to this, we output the full modeled directional spectra at a number of selected locations. The directional spectra are extracted every 10° across the globe (Fig. S2a), and for regional studies around Australia (Fig. S2b) and around Victoria, Australia (Fig. S2c). The model outputs are summarized in Table 4. The 3-hourly time step outputs are chosen to reproduce the peak sea states, crucial for accurate extreme value analyses (Lopatoukhin et al. 2000).

Table 4

WW3/ACM2 and WW3/EC3 model outputs.

Table 4

3. The historical wind-wave climate

To test the reliability of each climate run in simulating historical and future projected changes, we evaluate the WW3/ACM2 and WW3/EC3 climatology against benchmark observational and model datasets.

a. Comparison with satellite measurements

In this section we evaluate the WW3/ACM2 and WW3/EC3 10-m surface wind speed U10 and significant wave height Hs climatology against the Ribal and Young (2019) satellite altimeter dataset. The satellite altimeter observations are binned on a 2° × 2° regular grid. That is, all the calibrated and validated satellite measurements falling within each 2° grid cell are used to compute the monthly mean and 90th and 99th percentiles. These three monthly statistics are used to evaluate the WW3/ACM2 and the WW3/EC3 wind-wave climate models. The climate models are regridded on a 2° × 2° grid for the purpose of comparison with the satellite statistics. The satellite observations are available from 1985 to 2014 so this is the time window chosen for the comparisons. The percentile statistics are computed over the 1985–2014 time period with no averaging involved. Note that the altimeters are calibrated against in situ buoy winds which are extrapolated to a reference height of 10 m assuming a neutral boundary layer (Young and Donelan 2018).

Figure 2 shows the 1985–2014 significant wave height Hs climatology of both WW3/ACM2 and WW3/EC3. The mean Hs (Figs. 2a,d) have similar spatial distribution and magnitude. The WW3/EC3 90th- and 99th-percentile Hs (Figs. 2e,f) are higher than WW3/ACM2 (Figs. 2b,c), especially at the high latitudes of both the Northern and Southern Hemispheres. These are regions characterized by particularly rough seas, and the differences in the tail of the Hs distribution are a result of differences in the GCMs surface wind speed (Fig. S3).

Fig. 2.
Fig. 2.

The 1985–2014 significant wave height Hs climatology. WW3/ACM2 (a) mean, (b) 90th percentile, and (c) 99th percentile. (d)–(f) As in (a)–(c), but for WW3/EC3.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Figure 3 shows the 1985–2014 10-m surface wind speed U10 normalized biases between respectively the WW3/ACM2 (Figs. 3a–c) and the WW3/EC3 (Figs. 3d–f) climate statistics against the satellite altimeter observations. The mean WW3/ACM2 wind speed in the Northern Hemisphere is positively biased (10%–15%) in comparison with the satellite observed wind speed (Fig. 3a). In the Southern Hemisphere, the WW3/ACM2 performs better with the exception of slight positive biases in the trade winds region around 20°S. The WW3/EC3 mean wind climatology (Fig. 3d) shows low biases in the Northern Hemisphere with negative biases in the equatorial regions and a generally distributed negative bias of up to 10% in the Southern Hemisphere.

Fig. 3.
Fig. 3.

The differences in the 1985–2014 10-m surface wind speed climatology, ΔU10, between the climate models mean and percentiles compared with the same statistics found from the satellite altimeter measurements (Young and Ribal 2019). The contour plots show the normalized bias between WW3/ACM2 and altimeter (a) mean, (b) 90th percentile, and (c) 99th percentile. (d)–(f) As in (a)–(c), but for WW3/EC3 and altimeter. Red indicates model is higher than altimeter.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The difference between the climate models and the satellite observations increases at the extremes (90th and 99th percentiles). This is partly due to undersampling of satellite extremes (Young and Ribal 2019), especially at the highest 99th percentiles, and partly due to higher winds of the GCMs, as shown by comparisons with ERA5 winds in Fig. S3. Note that the satellite extreme wind speeds are smaller than ERA5 in the Northern Hemisphere, but larger in the Southern Ocean, suggesting low ERA5 extreme winds in the Southern Ocean (Liu et al. 2021).

In summary, compared to both satellite and ERA5 winds, the Northern Hemisphere shows the highest biases at the extremes, with both climate models showing stronger extreme winds, whereas in the Southern Hemisphere the WW3/EC3 99th percentile wind speeds (Fig. 3f) are high in some regions of the Southern Ocean, particularly south of the Indian Ocean. Overall, the climate models are relatively accurate in estimating the Southern Hemisphere surface wind climate. These results translate into a similar spatial distribution of the Hs normalized biases between the wave climate model runs and the satellite altimeter observations (Fig. 4). Spurious results are found in the sea ice covered regions as the satellite observations are sparse below 60°S.

Fig. 4.
Fig. 4.

As in Fig. 3, but for the significant wave height Hs climatology. The spurious data in the Antarctic sea ice-covered regions are caused by sparse satellite observations below 60°S and by the uncertainty of the model representation of the sea ice extent.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The mean Hs climatology comparison against the satellite altimeters (Figs. 4a,d) shows reasonably small biases (less than 5%). As is the case for the surface wind speed, the biases increase in the Northern Hemisphere extremes, showing the impact of the different extreme wind speeds. The bias is stronger in the WW3/EC3 simulations due to higher winds at the Northern Hemisphere mid- to high latitudes for that climate model. The WW3/ACM2, WW3/EC3, and the satellite Southern Hemisphere estimates compare well up to the 90th percentile. This is in contrast with the Northern Hemisphere where both climate models 90th percentile Hs values are consistently higher than the altimeter data. It is clear that the Northern Hemisphere satellite altimeter 90th percentile (ALT in Fig. S4) is also lower than ERA5. This is not the case in the Southern Hemisphere. We speculate that such a discrepancy between the Northern Hemisphere and Southern Hemisphere may be connected with the reduced seasonality of the Southern Hemisphere compared to the Northern Hemisphere (i.e., the difference between winter and summer Hs in the Northern Hemisphere is significantly larger than the Southern Hemisphere). In such a situation, the undersampling of the altimeter is likely to have a greater impact in the Northern Hemisphere.

b. Comparison with buoy and reanalysis data

To assess the WW3/ACM2 and WW3/EC3 seasonal climatology performance, we selected a number of U.S. National Data Buoy Center (NDBC) buoy measurements. The NDBC buoys are the longest and most continuous records of buoy observations available and thus well suited to evaluate the U10 and Hs climatology. Figure 5 show the NDBC buoys selected for the comparison based on the following criteria: more than 20 years of data, distance from the shore of more than 100 km and water depth of more than 300 m (i.e., deep-water conditions). The length of the record is crucial to evaluate the climatology and reduce the impact of interdecadal oscillations, which are generally simulated out of phase in the GCMs. The distance from the shore and the depth criteria ensure a robust comparison with deep-water conditions. Note that none of the buoys have a complete coverage over the full time span considered in the comparison with the climate models. As such, we checked the time series and verified that the missing data are evenly distributed between months. This avoids possible discrepancies in the monthly statistics shown in Figs. 6 and 7.

Fig. 5.
Fig. 5.

Selected NDBC buoys to investigate WW3/ACM2 and WW3/EC3 Hs and U10 monthly climatology. Red buoys are those selected for Figs. 6 and 7 monthly statistics comparison.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Fig. 6.
Fig. 6.

Comparison of the 10-m surface wind speed U10 monthly statistics of WW3/ACM2, WW3/EC3, and ERA5 with long-term NDBC buoy measurements from 1990 to 2014 (WMO41001, WMO42001, WMO46002). (a),(d),(g) U10 monthly mean, (b),(e),(h), U10 90th percentile, and (c),(f),(i) 99th percentiles. In each panel, a text box shows the number of data points analyzed from the model NTOT, the number of data available from the buoy Nb, the overall mean climatology at the location μ, and the overall climatology percentiles p90 and p99.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Fig. 7.
Fig. 7.

As in Fig. 6, but for the significant wave height Hs.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Figure 6 shows the results at three buoy locations representative of the general performance found in these tests (red point locations shown in Fig. 5). The comparison uses the 1990–2014 monthly U10 climatology for buoy WMO41001 in the North Atlantic, WMO42001 in the Gulf of Mexico, and WMO46002 in the North Pacific. The climate averages compare reasonably well with both the buoy observations and ERA5 data. At buoy WMO41001 (Figs. 6a–c; North Atlantic), the climate models clearly reproduce the seasonality of mean and extreme U10, as shown by the buoys and ERA5 data. Both climate models overestimate both mean and extremes, consistent with the results for the altimeters in Fig. 3. The same general result is also apparent at buoy WMO46002 (Figs. 6g–i; North Pacific), although the climate models are generally in better agreement with the buoy and ERA5 data at this location.

In the enclosed basin of the Gulf of Mexico (WMO42001; Figs. 6d–f) the comparison shows higher discrepancies. The WW3/ACM2 U10 is biased high in summer, with an unusual peak in July. This discrepancy is clearly enhanced at the extremes (Figs. 6e,f). Further investigation is needed to understand the July differences in the WW3/ACM2 extremes. The WW3/EC3 shows lower extreme values when compared to buoy measurements and ERA5 results. This is arguably related to the GCMs’ coarse wind horizontal resolution, which means that tropical cyclone (TC) peak winds are not adequately resolved. Clearly, the performance of both climate models in this enclosed region are poorer than the open ocean comparisons.

The comparisons of Hs between the climate models and buoy and ERA5 data (Fig. 7) show similar results to the wind speed comparisons. For both climate models the mean Hs climatology compares particularly well with in situ and ERA5 observations (Figs. 7a,d,g) with yearly average differences of less than 20 cm. The extremes show the same discrepancies found in the wind speed. Note that both climate models miss the peaks in the summer TC season at WMO41001 and WMO42001 (Figs. 7c,f).

The reader is referred to Figs. S5–S9 and S11 for further comparisons of the WW3/ACM2 and WW3/EC3 models against ERA5 results (Hersbach et al. 2020) and the Liu et al. (2021) ST6 hindcast. Throughout the remainder of this paper, we present the mean and peak period comparison with ERA5 as the reference model.

c. The mean and peak wave period

An accurate assessment of the wind-wave climate cannot disregard the wave period, which plays a fundamental role in many coastal processes and ocean engineering applications. In Fig. 8 we compare the mean WW3/ACM2 and WW3/EC3 Tm,02 and Tp periods against ERA5. We regard ERA5 as the best available dataset to compare the wave periods as it is the most recent global reanalysis. Figures 8a and 8e show the Tm,02 1985–2014 climatology for the climate models. The longest waves are found in the Southern Hemisphere where the Southern Ocean extended fetches and strong winds all year round generate average mean periods of up to 8 s. The WW3/ACM2 Tm,02 compares particularly well with ERA5 (Fig. 8b) with absolute normalized biases of less than 5%. The Tm,02 biases against ERA5 are slightly higher for WW3/EC3 (Fig. 8f), with an overall positive bias except in the North Atlantic.

Fig. 8.
Fig. 8.

The 1985–2014 mean period Tm,02 and peak period Tp climatology for (a),(c) WW3/ACM2 and (e),(g) WW3/EC3. (b),(f) and (g),(h) The normalized bias between (b),(d) WW3/ACM2, (f),(h) WW3/EC3 and the reference ERA5 dataset. Red indicates climate model has longer wave period than ERA5. The ERA5 mean and peak periods climatology is shown in Fig. S8.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Figures 8c and 8g show the Tp 1985–2014 climatology. The peak wave period is a particularly challenging parameter to model and measure, as it is defined by the spectrum peak frequency, which is sensitive to sudden peak shifts between wind-sea and swell sea states. The longest peak periods are found at the Southern Hemisphere low latitudes, representative of swells propagating from the high-latitude storm regions. The comparison of Tp results with ERA5 (Figs. 8d,h) show marked differences in the peak period in the eastern equatorial regions of both the Pacific and Indian Oceans. In these regions, several sea states coexist. Such regions are known to be swell-dominated, which means that there are generally light local winds and the majority of the wave energy is in the form of swells propagated from distant higher-latitude storms. The Tp bias compared to ERA5 is stronger for WW3/EC3 than WW3/ACM2, as shown in Fig. 8. As these regions are swell dominated, an obvious conclusion is that the differences are associated with the swell generation regions in the Southern Ocean. However, the bias in WW3/EC3 is actually at a maximum during the Southern Hemisphere summer (Fig. S11) [December–February (DJF)]. As this is a period of reduced Southern Ocean swell, this suggests the causes of the bias are more complex. In fact, small variations of the spectra could lead to significantly different peak period values describing different wave systems.

To further investigate the reasons behind these marked differences in Tp shown in Figs. 8d, 8h, and S10, we make use of the directional spectra extracted from the model. Figure 9 shows the 2010–14 directional spectra average climate for WW3/ACM2 and WW3/EC3 at two selected locations. We limit our spectra analysis to this time window for computational constraints after verifying that the 2010–14 Tp statistics show the same differences with ERA5 found for the 1985–2014, 30-yr period (Figs. 8d,h). Specifically, we select location A (10°S, 90°E) and location B (10°S, 120°W) shown in Fig. 9, derived from the 10° global point outputs (Fig. S2a).

Fig. 9.
Fig. 9.

The 2010–14 average directional spectra comparison at two different locations close to the equator. The point locations chosen, A and B, are shown in the global map. (a)–(d) The directional spectra for location A in the equatorial Indian Ocean are shown. (e)–(h), The directional spectra for location B in the equatorial central Pacific are shown. (top) DJF Southern Hemisphere summer season (a),(e) WW3/ACM2, (b),(f) WW3/EC3. (bottom) Average spectra for the JJA Southern Hemisphere winter season for (c),(g) WW3/ACM2 and (d),(h) WW3/EC3. The angles 0°–360° refer to the direction of propagation of the waves. Note that the wave direction follows the oceanographic convention (i.e., wave propagation toward the direction). The radial axis is the wave period expressed in seconds. A smaller wave period, i.e., energy closer to the center of the graph, denotes a wind-dominated sea (wind-sea). A larger wave period, i.e., energy farther away from the center of the graph, describes swell systems.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The graphs in Fig. 9 show the directional distribution of the wave energy density (m2 s rad−1), with 0° referring to the geographic North. The left half of the figure (Figs. 9a–d) shows the average directional spectra at location A in the Equatorial Indian Ocean, and the right half (Figs. 9e–h) at location B in the equatorial Pacific Ocean. The first row of the directional spectra shows the DJF averages. The second row is the June–August (JJA) averages. Both locations reach their most energetic sea states in the Southern Hemisphere winter season (JJA), with the wind-wave climate in the equatorial Indian Ocean being more energetic than the equatorial Pacific. The highest energy is found in the WW3/EC3 run (Fig. 9d), which is characterized also by generally longer Tp than the WW3/ACM2 (Fig. 9c). Most of the energy comes from the southwest, suggesting this is the impact of high-latitude winter JJA storms. The fact that these swell systems are stronger in WW3/EC3 than WW3/ACM2 is consistent with the higher wave energy in the Indian Ocean basin of the Southern Ocean seen in Figs. 4a and 4d for WW3/EC3. The spectra also show a lower energy wind-sea (smaller periods) originating from the southeast. In this case, the WW3/ACM2 is more energetic than the WW3/EC3 as the local ACM2 winds are stronger (see Figs. 3a,d).

In the Southern Hemisphere summer (DJF) the equatorial Pacific Ocean (Figs. 9e,f) is more energetic than the equatorial Indian Ocean (Figs. 9a,b). In this case, a third SE sea state appears, characterized by long period waves generated NW of this location. The WW3/EC3 SE sea state (i.e., waves propagating toward the SE, Fig. 9f) is more energetic and with a slightly longer period than the corresponding WW3/ACM2 case (Fig. 9e). This is consistent with the biases seen in Fig. 8d. These SE sea state Tp differences between WW3/ACM2 and WW3/EC3 are related to the differences between the two GCMs’ Northern Hemisphere high-latitude wind speeds. In particular the EC3 wind extremes are stronger than ACM2 (Fig. S3) and as a consequence, the WW3/EC3 sea states are more energetic (Fig. S4), which means more energetic swell systems in the Pacific equatorial regions (Figs. 9e,f). It is also interesting to note that the DJF northeast sea state is stronger in WW3/EC3. This is because the Southern Ocean EC3 winds are stronger than the ACM2 winds (Fig. S12a). This is in contrast with the JJA season where the NE sea state is more energetic in the WW3/ACM2 directional spectra due to the stronger ACM2 GCMs winds at around 50°S.

In conclusion, the possibility to examine the climate models’ directional spectra allows us to perform an in-depth analysis of the wind-wave climate. This analysis is extremely valuable to understand the wind-wave climate and the performance of GCM downscaling approaches, further highlighting the added value of the products extracted from the present wind-wave climate runs.

d. Historical wind-wave climate model performance

The comparison with different observational datasets shows that the WW3/ACM2 and the WW3/EC3 climate models represent well the mean U10 and Hs climatology over the 30-yr 1985–2014 reference period. The global U10 average bias compared to satellite observations is −5% for ACM2 and −8.7% for EC3. The global Hs average bias is −6% for ACM2 and −5.75% for EC3. The comparison with more than 20 years of buoy observations in the Northern Hemisphere showed that the wave climate models represent well the seasonality in the open ocean. However, there are still significant limitations in representing the wave climate in enclosed seas and tropical cyclones regions (Figs. 6c,e,f). Further effort is needed to increase the GCMs resolution as well as improve the physics for an accurate simulation of tropical cyclones and wave climate in enclosed basins. In the North Atlantic and the North Pacific oceans, the comparison of the ACM2 and EC3 U10 90th (99th) percentiles show a bias of up to 20% (30%) for ACM2 (Figs. 3b,c) and up to 30% (40%) for EC3 when compared to satellite measurements (Figs. 3e,f). This is consistent with a general tendency of CMIP6 models to show an equatorward bias both in the North Pacific and the North Atlantic (Priestley et al. 2020). Note that the biases found at the 90th percentile and particularly at the 99th percentile are partly caused by satellite underestimation of extremes. This is also depicted in the comparison between ERA5 and altimeter climatologies in Fig. S3. Interestingly, the North Pacific extratropical storms positive bias (Fig. 3) impacts also the directional spectra climatology in the tropical regions (Figs. 9e,f). In the Southern Hemisphere both ACM2 and EC3 U10 extremes are remarkably similar to what has been observed by satellite altimeters over the 1985–2014 period (Figs. 3a,b). The EC3 model shows slightly higher Southern Ocean U10 extremes (Fig. S3), that cause larger wave height percentiles (Figs. 4e,f) and wave periods (Figs. 8f,h) than the WW3/ACM2 simulation. Overall, the evaluation of the WW3/ACM2 and WW3/EC3 historical wave climate provides confidence for use of the models to study future projected changes in future wind and wave climate.

4. CMIP6 WW3/ACM2 and WW3/EC3 evaluation against comparable models

There are significant datasets from a variety of CMIP5-forced models available and a comprehensive review of the available CMIP5-forced datasets is presented in Morim et al. (2018) and further analyzed for climate change impact by Morim et al. (2019). Our interest is to evaluate the performance of the two CMIP6-forced global wave models produced in this work in representing the historical climate comparing the results with the corresponding CMIP5 GCM-forced wave climate models. To achieve this, we compare the climate simulations performed with earlier versions of the ACCESS and EC-Earth GCMs, with the WW3/ACM2 and WW3/EC3 runs. We expect that the improved representation of atmospheric dynamics of the CMIP6 GCMs will improve the surface wind speed representation and, as such, the wind-wave climate simulations. Also, despite a large intermodel spread, the CMIP6 GCMs show an overall mean sea ice concentration and extent closer to the historical observations than earlier GCMs (Roach et al. 2020). Sea ice is of particular interest for the present model set up which includes the polar regions. The continuous 140-yr multimodel runs also provide a unique dataset to understand future climate impacts. Although the present comparisons are an important initial step, a thorough evaluation of CMIP6 derived wind-wave climate models can only be achieved with a full ensemble of models. Thus, a complete analysis of the wind-wave climate performance of the CMIP6 forced models’ in comparison with the COWCLIP CMIP5 ensemble is planned for future work on an eight-model CMIP6 ensemble, presently under development.

WW3/ACM2 and WW3/EC3 comparison with corresponding CMIP5-forced wave models

Figures 10a–h shows the normalized bias against ERA5 of the 1979–2004 historical climatology for all the wind-wave model simulations forced by different versions of ACCESS and EC-Earth winds, available from the COWCLIP dataset. In this comparison, we exclude the statistical approach followed for the ACCESS models by Camus et al. (2017) and focus only on the dynamical studies. The different GCM-forced wave simulations are not only performed with different phases of the GCMs but also with different wave models. Figures 10a and 10b shows that WW3/ACM2 and WW3/EC3 compare well with ERA5 and have generally lower biases in comparison with previous CMIP5 simulations (Figs. 10c–h). Both WW3/ACM2 and WW3/EC3 show a similar positive bias in the Southern Ocean region from 60° to 150°E. This bias was found also in Meucci et al. (2020b) CMIP5 ensemble down-scaled wave results and might be related to the GCMs mean sea level pressure gradients. The CMIP5 models (Figs. 10c–h) generally have global positive biases associated with generally higher winds for these GCMs, with the exception of the ACCESS1.0 CSIRO run (Fig. 10c). The highest biases for WW3/ACM2 and WW3/EC3 against ERA5 are found in the sea ice regions. This is related to the strong uncertainties in modeled sea ice concentrations both in climate models and reanalyses (Hersbach et al. 2020; Roach et al. 2020). However, the representation of the sea ice regions is still a significant advance in the present modeling compared to the older CMIP5 wind-wave global climate models, which excluded these regions (Fig. 10).

Fig. 10.
Fig. 10.

Comparison of the 1979–2004 average significant wave height differences ΔHs between wave climate models and ERA5 (bias relative to ERA5: red indicates climate model is higher than ERA5). Results represent (a),(b) the present CMIP6 wind-wave climate runs, (c)–(h) all the CMIP5 runs available for the Australian ACCESS and European EC-Earth forced wave models (Morim et al. 2019), and (i) the CMIP6 FIO-ESM v2.0 (Song et al. 2020). Each plot title describes: the CMIP phase, the research institute where the climate runs were performed, the GCM chosen, the wave model (WW3 or WAM), and the wave model settings (physics packages of WW3 such as ST3, ST4, ST6, or WAM cycle).

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Table 5 shows the global Hs bias, the Spearman ρ correlation, and the Root-mean-square Error (RMSE) for each model of Fig. 10 compared with ERA5. The WW3/ACM2 and WW3/EC3 statistics are computed excluding the polar regions to form a consistent comparison with the statistics of the CMIP5 wind-wave models. The major improvement of the WW3/ACM2 and WW3/EC3 models is in the bias. The CMIP6-forced model runs show a maximum bias of 3 cm whereas the CMIP5 models show global biases of more than 10 cm. The Spearman correlation and the RMSE scores also show a slight improvement of the CMIP6 models over the majority of the CMIP5 models. Figure 11 compares the global probability distribution functions of each model in Table 5. We find a good overall agreement at all sea states (Hs) of the two CMIP6 models with ERA5, especially for the WW3/ACM2 model. In general, there is a modest but discernible improvement of the CMIP6 models compared to the CMIP5 models in reproducing the observed historical climate.

Fig. 11.
Fig. 11.

Comparison of the 1979–2004 global probability distribution function of significant wave height Hs. Results are shown for all CMIP6 and CMIP5 models shown in Fig. 11. ERA5 probability distribution function is shown in black.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

Table 5

The CMIP6 and CMIP5 global wave statistics computed from the comparison of the 1979–2004 significant wave height Hs against ERA5. The columns show the overall bias in meters, the Spearman correlation coefficient (ρ), and the root-mean-square error (RMSE).

Table 5

We further compare the WW3/ACM2 and WW3/EC3 performance with the recent FIO-ESM v2.0 long-term CMIP6 wind-wave model (Song et al. 2020) (Fig. 10i). The FIO-ESM v2.0 performs well in the Southern Ocean but is biased high at the mid- to low latitudes in comparison with ERA5 (Fig. 10i).

5. Global trends

a. CMIP6-forced models historical trends evaluation

One of the main questions surrounding the statistical analysis of the global wind-wave climate is how well the GCM-forced wave climate models reproduce historical trends. The benchmark datasets to evaluate such trends are reanalyses and satellite altimeter observations. The trends derived from these datasets are affected by uncertainty, as reanalysis time series have discontinuities caused by a different number of observations assimilated throughout the years, and changes in the level of accuracy of the assimilated observations (Wohland et al. 2019; Meucci et al. 2020a). Similarly, satellite altimeter trends depend on the calibration procedure followed and the number of missions considered (Timmermans et al. 2020; Young and Ribal 2022). Nonetheless, these are crucial products to understand if the GCM-forced wave climate models show plausible trends.

As in Meucci et al. (2020a), we use the nonparametric Theil–Sen trend estimator (Theil 1950; Sen 1968), since it is a robust methodology for nonnormally distributed data. The trend magnitude is found as the median of the monthly Sen slopes [Eq. (2)]:
median(XjXitjti),1ijn,withij,
where n is the number of years, Xj and Xi are the Hs monthly mean values, tj and ti the times of the observations in years. To test the significance of the trend across the globe we use the Mann–Kendall test adapted to account for seasonality and serial dependence (Hirsch et al. 1982; Hirsch and Slack 1984). We use this approach in continuity with previous wind-wave trend studies (Aarnes et al. 2015; Meucci et al. 2020a). Note that here, and in previous studies, statistical testing is applied to individual grid cells and neglects their spatial dependence. Large numbers of independent tests inevitably result in some number of erroneous rejections of the null and may lead to an overestimation of the statistical significance of the trend results (Wilks 2016). In addition, the intrinsic spatial dependence of Hs may further exacerbate this issue. Therefore, the statistical significance shown here, as in previous studies, should be interpreted with caution.

Figure 12 shows the comparison of the WW3/ACM2 and WW3/EC3 historical climate trends with both satellite altimeter (Ribal and Young 2019), and ERA5 (Hersbach et al. 2020) trends. The trends are computed over the 1985–2014, 30-yr historical period and shown as percentage per decade with the statistically significant regions at the 5% significance level hatched in black (Fig. 12).

Fig. 12.
Fig. 12.

Comparison of the 1985–2014 Hs global trends (% decade−1) between (a) the Young and Ribal (2019) altimeter dataset, (b) ERA5 (Hersbach et al. 2020), and the wave climate models (c) WW3/ACM2 and (d) WW3/EC3. Individual grid cells found to be statistically significant at the 5% level are hatched in black.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

ERA5 generally shows the largest increasing trends (Fig. 12b). These large positive trends are partly spurious as a consequence of the discontinuities resulting from the assimilated observations (Meucci et al. 2020a). However, all model datasets (Figs. 12b–d) show a clear Hs increase in the Southern Hemisphere across the 30-yr period. To some level, this signal is also apparent in the altimeter results (Fig. 12a). It is worth noting that the Ribal and Young (2019) altimeter dataset calibration procedure produces smaller trends in comparison with the Dodet et al. (2020) data, as shown by Timmermans et al. (2020). Also, all datasets show a general Hs decrease in the North Pacific ranging from −4% decade−1 in the altimeter results (Fig. 12a), to −1% decade−1 in the WW3/ACM2 results (Fig. 12c). The main differences between the climate models and the altimeter and ERA5 trend results are found in the North Atlantic. Further investigation is needed to understand why the GCMs show a decreasing trend in the North Atlantic, which is in contrast with what is observed by the satellites over the same time period. Overall, the WW3/ACM2 and the WW3/EC3 trend results show the potential of the present long-term wave climate simulations in representing a realistic climate change signal, thus adding confidence that the future projections will also produce plausible trends.

b. 140-yr wind-wave climate trends

The 140-yr continuous wind-wave climate time series produced are an ideal long-duration dataset to perform robust trend analyses. The possibility to analyze a dataset that spans across two centuries allows us to significantly reduce the impact of interdecadal oscillations in favor of long-term climate signals. We perform a trend analysis on the monthly mean and monthly 99th-percentile Hs time series derived from the WW3/ACM2 and the WW3/EC3 3-hourly model outputs.

Figure 13 shows the trend analysis results for WW3/ACM2 (Figs. 13a–d) and WW3/EC3 (Figs. 13e–h) 140-yr projections, for SSP1–2.6 (Figs. 13a,b,e,f) and SSP5–8.5 (Figs. 13c,d,g,h) scenarios in terms of percentage change per decade. The gray hatching refers to statistically significant trends at the 5% significance level. The results show that the trends are statistically significant in extended regions of the global oceans, in particular for the high-emission scenario (SSP5–8.5). The extent of the gray hatched statistically significant regions is smaller in the SSP1–2.6 scenario (Figs. 13a,b,e,f). Nevertheless, for both cases the use of the long-duration projections means that a much larger percentage of the globe has statistically significant results compared to previous shorter duration and time-slice experiments (Hemer and Trenham 2016; Casas-Prat et al. 2018; Morim et al. 2019; Meucci et al. 2020b).

Fig. 13.
Fig. 13.

The 1961–2100 Hs global trends (% decade−1). WW3/ACM2 (a),(b) SSP1–2.6 and (c),(d) SSP5–8.5, and WW3/EC3 (e),(f) SSP1–2.6 and (g),(h) SSP5–8.5. Individual grid cells found to be statistically significant at the 5% level are hatched in gray.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The most significant changes in the wind-wave climate are found in the Southern Ocean, the tropical eastern Pacific, and the two Northern Hemisphere ocean basins. The absolute Sen slope values are larger for SSP5–8.5 than SSP1–2.6. WW3/ACM2 shows larger increasing trends in the tropical eastern Pacific and the Southern Ocean wind-wave climate than WW3/EC3. In general, in the Southern Hemisphere the WW3/ACM2 shows larger increasing trends than WW3/EC3. Conversely, in the Northern Hemisphere the WW3/EC3 decreasing trends are stronger than the corresponding WW3/ACM2 trends. The largest absolute values of the trends are found at the high latitudes of both the Northern and the Southern Hemispheres, connected with the projected poleward shift of the surface wind climate already observed in both CMIP5 (Chang et al. 2012) and CMIP6 models (Goyal et al. 2021). The magnitude of the percentage changes in the extremes is comparable to the percentage changes in the mean values, with similar spatial distribution. However, the positive trends in the Southern Ocean are stronger for the higher emission scenario (SSP5–8.5). The regions of the ocean where there is sea ice for most of the year are excluded from the trend analysis as the high number of null data months affects the trend calculations.

6. Wind-wave climate evolution by climatic regions

Continuous long-term downscaled climate simulations have the potential to improve the quality and clarity of historical and future projected wind-wave climate analyses across the globe. Within this context, one of the objectives of this paper is the regional synthesis of future projected wind-wave climate following the Iturbide et al. (2020) IPCC updated global climatic regions. Using the Python regionmask library (https://regionmask.readthedocs.io) we plot the WW3/ACM2 and WW3/EC3 10-yr running lagged mean Hs anomalies weighted by latitude over each climatic region (Fig. 14). The anomalies are calculated relative to the 1985–2014 reference climate for each model. The global distribution of the 1985–2014 Hs climatology is shown in Fig. 2. Figure 14 compares the WW3/ACM2 (red lines) and the WW3/EC3 (blue lines) SSP1–2.6 and SSP5–8.5 with the FIO-ESM2.0 (Song et al. 2020) SSP1–2.6 (lavender line) and SSP5–8.5 (violet line), and a CMIP5 47-model ensemble (black line) selected from the COWCLIP2 RCP8.5 dataset (Morim et al. 2019, 2020b). Note that, only the models with readily available monthly means and monthly 90th and 99th percentiles were selected from the COWCLIP2 dataset. The COWCLIP 47-model ensemble is available only for two time slices: The 1979–2004 and the 2081–2100. In this case, the anomalies are computed against the 1979–2004 reference climate and only for the RCP8.5 scenario. The CMIP5 anomalies are plotted to compare previous CMIP models with the newly upgraded CMIP6 long-term continuous wind-wave models. When compared to the CMIP6 model anomalies, the COWCLIP2 47-model ensemble average anomalies show generally smaller future projected changes, arguably due to the equal-weight model averaging method followed (see Fig. S17).

Fig. 14.
Fig. 14.

The 1961–2100, 140-yr time series averaged over the latest IPCC climate reference regions (Iturbide et al. 2020). The Hs anomalies are shown as 10-yr running means. The anomalies are with reference to the 1985–2014, 30-yr climate averages of each respective CMIP6 model. The CMIP5 ensemble reference climate is 1979–2004.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The anomalies in the mean Hs climate (Figs. 14 and S14) highlight four regions where the projected changes are most significant across the twenty-first century: the Arctic, the North Pacific, the North Atlantic, and the Southern Ocean. Similar changes are observed at the 90th (Fig. S15) and 99th (Fig. S16) percentiles. The percentiles are computed for each year and a 10-year running lagged mean is performed on the yearly percentile anomalies time series. This is also in accordance with the global decadal trends in Fig. 13. These regions show changes of the mean Hs climate from the reference climatology exceeding 20 cm in the SSP1–2.6 runs and 30 cm in the SSP5–8.5 scenarios by the end of the twenty-first century. Regional extremes trend values (Figs. S15 and S16) are larger than the mean wave climate (Figs. 14 and S14), but, as shown in Fig. 13, the mean and extremes percentage changes are consistent.

The Arctic Ocean anomalies show marked fluctuations in wave climate, largely due to the reduction in sea ice coverage in the area (Meredith et al. 2019). In addition to these fluctuations there is, however, a clear increasing trend in this region for both the SSP1–2.6 and SSP5–8.5 scenarios in all models. This is caused by the warming climate effect on the Arctic region, which is predicted to be ice free in some months of the year by 2050 (Fox-Kemper et al. 2021).

In contrast, the North Pacific and North Atlantic regions are characterized by a decrease in significant wave height for the high-emission SSP5–8.5 scenarios for all models (WW3/ACM2, WW3/EC3, FIO-ESM2.0 and the CMIP5 ensemble). A different picture emerges for the SSP1–2.6 scenario cases where the anomalies have a slight decrease until the mid-twenty-first century but then revert to historical levels.

While the Northern Hemisphere wind-wave climate shows general climate stability for the SSP1–2.6, the Southern Ocean shows an increase in the wind-wave climate across all models and scenarios. This trend is connected to the projected increasing intensity of the prevailing westerlies and their poleward movement (Chang et al. 2012; Goyal et al. 2021). The particularly low anomalies for the CMIP5 ensemble (black line) in the Southern Ocean plot (region 57 in Fig. 14) are caused by low climate change signals of some of the wave climate models contributing to the ensemble average (Fig. S17). Note that the CMIP5 model ensemble (Morim et al. 2020b) domain extent, from 79.5°N to 79.5°S, and sea ice concentration biases could also play a significant role.

A detailed analysis of the internal variability of the 140-yr climate dataset is planned for a future study. Here, we compare the wind-wave climate in the Southern Ocean with the Southern Annular Mode (SAM) oscillation, also known as the Antarctic Oscillation (AAO). The SAM index (SAMI) is defined as the difference of zonal mean sea level pressure between 40° and 65°S following Gong and Wang (1999), and standardized relative to 1979–2004 climatology. A comparison for the Southern Ocean with the 10-yr SAMI running means for the ACM2 and EC3 GCMs shows that the positive trend in Southern Ocean Hs coincides with the trend in the SAMI yearly mean anomalies (Fig. 15a). Also, a strong correlation is found between the interdecadal atmospheric oscillation (SAMI) and the Southern Ocean wind-wave climate (Fig. 15). Note that, around 2070 the ACM2 and EC3 SAMI lines separate. Similar changes in slope can also be observed in the Hs anomalies (Fig. 15a). The WW3/EC3 SSP5–8.5 Hs anomalies have a sudden increase after 2060, vice versa, the WW3/ACM2 Hs anomalies reach a plateau after 2060 and then have a sharp increase halfway through the 2080s. To isolate the connections between the SAM and the wind-wave climate we detrended both the SAMI and the Hs anomalies in the Southern Ocean region (Iturbide et al. 2020). Figures 15b and 15c show the correlation between the detrended SAMI and detrended Hs yearly mean and detrended 99th-percentile anomalies, respectively. The plots clearly show the connection between the wind-wave climate and the SAM in the Southern Ocean region both for the mean and extremes climatology.

Fig. 15.
Fig. 15.

The 1961–2100 ACM2 and EC3 Southern Annular Mode index (SAMI) 10-yr running means. (a) Comparison between the SAMI and the Hs mean climate 10-yr running mean anomalies in the Southern Ocean climatic region (Iturbide et al. 2020). (b),(c) Detrended SAMI compared with (b) the detrended Hs mean climate anomalies, and (c) the detrended Hs 99th-percentile anomalies.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The ACM2 and EC3 GCMs show significantly different phases of the SAM (Fig. 15). These results highlight the importance of analyzing long-term wind-wave climate evolution and the advantages of a 140-yr continuous wind-wave climate dataset. Interdecadal effects in different GCMs have differing phase and hence limited duration time slice comparisons may yield divergent results, depending on the phase of the interdecadal oscillations. To date, statistical analyses of future projected wind-wave climate are mostly based on time slices (Hemer et al. 2013; Morim et al. 2019; Meucci et al. 2020b), and Fig. 15 suggests that the results of these studies could be impacted by interdecadal oscillations.

7. Global wind-wave climate future projections

In this section we evaluate the global projected changes of future wind-wave climate, comparing two 30-yr time slices, the historical 1985–2014 period, hereafter HIST, and the end of the twenty-first century, 2071–2100, SSP5–8.5 scenario, hereafter END21C. The projected changes are shown as normalized changes over the historical climatology, Δ = (END21C − HIST)/HIST for the following wind-wave parameters: The 10-m surface wind speed U10, the significant wave height Hs, the mean second-order period Tm,02, the peak period Tp, the mean wave direction θ¯, and the peak wave direction θp. A similar global distribution of the changes in wind-wave climate by the end of the twenty-first century is found for the middle emission scenario SSP1–2.6, although the magnitude of the changes are reduced. This is consistent with the long-term trend results shown in Fig. 13.

The 30-year time scale is an improvement from previous CMIP5 studies which were mostly limited to 20-year time slices at the end of the twenty-first century. A sensitivity analysis on the changes in significant wave height between three different time slice extents, 40-year (2061–2100 minus 1975–2014), 30-year (2071–2100 minus 1985–2014), and 20-year (2081–2100 minus 1995–2014) shows no major differences in the global significant wave height normalized changes ΔHs (Fig. S18). A small signal of the interdecadal oscillations impact on the time slice climate statistics can be observed in the Indian Ocean and in the Equatorial and North Pacific oceans, especially in the WW3/EC3 model climatologies (Figs. S18d–f). The time-slice comparisons represent a useful metric to evaluate projected wave climate change. The historical period chosen is 1985–2014 in accordance with the climate model evaluation performed in section 3.

a. Surface wind speed

The main driver of the wave climate is the wind speed. Figure 16 shows the normalized differences (Δ) between the END21C and the HIST slices. The plot shows the ΔU10 mean, 90th and 99th percentiles for WW3/ACM2 (Figs. 16a–c) and WW3/EC3 (Figs. 16d–f). Both models show a clear signal of change in the westerlies, both in the Northern and Southern Hemispheres. The spatial distribution of the increasing wind speed in the tropics is different between the two models. We speculate this is related to different Pacific interdecadal oscillation phases. Note that, if we compare the changes in the mean wind speed ΔU¯10 (Figs. 16a,d) between the GCMs, the largest changes in ACM2 wind speed are focused in the central region of the Pacific Ocean, whereas for EC3 the largest changes are located more to the west, close to Papua New Guinea and Indonesia. The same pattern occurs at the higher percentiles; however, the signal of change is less clear as the magnitude of change is approximately the same and the percentage values decrease accordingly. Both polar regions experience an increase in the wind speed by the end of the twenty-first century (Fig. 16) as the westerlies move poleward and increase in intensity Toggweiler (2009). These changes have an impact on the wave direction, particularly of the Southern Hemisphere, as also shown in Figs. 20 and S9. In the Northern Hemisphere the increasing westerlies, combined with the sea ice retreat, mean that larger regions of the ocean will be subjected to stronger winds. As a result, the Arctic regions are projected to show a general increase in wave climate.

Fig. 16.
Fig. 16.

Surface 10-m wind speed U10 percentage changes between two 30-yr slices: 1985–2014 and SSP5–8.5 2071–2100. WW3/ACM2 (a) mean, (b) 90th percentile, and (c) 99th percentile, and (d)–(f) WW3/EC3.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

b. Significant wave height

Changes in the significant wave height Hs are largely a consequence of the changes in the surface wind speed U10. However, waves generally have a slightly different spatial distribution. An accurate analysis of the global sea states and its changes must consider all the major wind-wave parameters (significant wave height, wave period, and wave direction). Figure 17 shows the ΔHs normalized changes between the END21C and the HIST time slices for the mean and 90th and 99th percentiles of WW3/ACM2 (Fig. 17a–c) and WW3/EC3 (Fig. 17d–f).

Fig. 17.
Fig. 17.

As in Fig. 16, but for the significant wave height Hs.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The largest Hs changes are found at the high latitudes of both hemispheres, particularly in the polar regions, with a marked increase in the Hs in both Arctic and Antarctic regions by the end of the twenty-first century SSP5–8.5 scenario.

The normalized ΔHs changes are consistent across all statistics, that is mean and extreme values. The WW3/ACM2 and WW3/EC3 changes are similar, with the exception of a slightly different spatial distribution, evident in the South Pacific. Again, these differences may be related to different interdecadal oscillation phases modeled by the different GCMs. It is clear that the future projected changes in the high-latitude winds will impact each hemisphere ocean wave climate differently. The Northern Hemisphere high latitudes are mostly covered by land and, as such, even if the winds are projected to increase and move poleward, no major effect is seen on the ocean wave climate at the lower latitudes. In contrast, the Southern Hemisphere Earth’s high latitudes are mostly land-free (Southern Ocean), and the increasing wind intensity causes more pronounced changes in the wave height.

Other regions, such as the Northeast Pacific adjacent to the Canadian and U.S. west coasts, show differences between the two models at the extremes. To better understand the global Hs changes we select a number of locations around the globe and analyze the probability distribution function differences for different time slices across the 140-yr simulation period. Figure 18 shows the Hs probability distribution changes moving from the historical period to the end of the twenty-first century SSP5–8.5 scenario, as derived from the 3-hourly WW3/ACM2 and WW3/EC3 model outputs. Such changes are shown at selected locations where the two wave climate models show different changes (Fig. 17), or where there are interesting changes in the wind-wave climate variability. The probability distribution colors gradually change from dark to light evolving from the historical period to the future SSP5–8.5 projected scenario. The probability distributions are shown in shades of red for WW3/ACM2 and in shades of blue for WW3/EC3. For clarity purposes boxplots are shown only for the historical 1961–84 and the future 2071–2100 time periods.

Fig. 18.
Fig. 18.

The 1961–2100 Hs probability distribution changes at different point locations of the global oceans. The point locations are marked by an orange dot inside their respective climatic regions in the maps at the top of the figure. The future projections refer to the SSP5–8.5 scenario. The probability distributions are shown in different shades from dark (historical decades) to light colors (future projected decades). (a)–(e) WW3/ACM2 and (f)–(l) WW3/EC3. The boxplots compare the 1961–84 (dark colors) and 2071–2100 (light colors) time periods, and show the median value, the interquartile range (IQR = Q3 − Q1, with Q1 = 25th percentile and Q3 = 75th percentile), and the lower (Q1 − 1.5 × IQR) and upper (Q3 + 1.5 × IQR) whisker values.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

The first location (Figs. 18a,f) is in the region between the Southern Ocean and the Indian Ocean (40°S, 100°E). Both model distributions show a gradual decrease in wave climate across the different decades. However, the upper whiskers of the box plots show opposite changes between the models at the Hs extremes. In WW3/EC3 the extremes are increasing but the bulk of the distribution is decreasing with an increasing variance in the data. For WW3/ACM2, however, there is a decrease in wave climate at all percentiles.

In both WW3/ACM2 and WW3/EC3 there is a consistent Hs decrease in the North Atlantic (35°N, 300°E; Figs. 18b,g). The narrowing probability distribution curves and the boxplots’ interquartile ranges (IQR; i.e., the difference between 75th and 25th percentiles) show that, unlike the Southern Ocean, there is also a decrease in the variance of the future projected Hs. The same changes can be observed in the northwest Pacific location (30°N, 150°E; Figs. 18c,h). Conversely, in the northeast Pacific (45°N, 210°E; Figs. 18d,i) there is a general decrease but the variance of the data at the end of the century is similar to the historical period, as shown by the similar IQR widths.

We also investigated a point location in the Indian Ocean (20°S, 80°E; Figs. 18e,l). Note that the WW3/ACM2 shows a slight general decrease in the wind-wave climate, whereas the WW3/EC3 changes are mainly confined to the variance. That is, the WW3/EC3 future projected Hs has a larger IQR in parallel with more intense extremes.

The results in Fig. 18 show that changes to the projected wind-wave climate are not confined to increases in mean and percentile conditions across the 140-yr period. These changes may also result in differences in wave climate variability at specific locations.

c. Mean and peak period

An important parameter for coastline erosion studies and marine structures is the wave period. The wave height together with the wave period and the wave direction allow estimates of the possibility of occurrence of wave breaking, crucial for wave loads on structures. Wave periods are also particularly important for floating structures to avoid resonant motion (Ochi 2005). Furthermore, the knowledge of the height, period. and direction of the waves gives us an understanding of the coastal erosion and accretion patterns (Davidson-Arnott et al. 2019), and estimating the changes in the future is crucial for coastal adaptation strategies. Here, we analyze the impacts of the changing climate on the mean wave period and the peak wave period statistics. Figure 19 presents the ΔT normalized changes for the second-order mean wave period ΔTm,02 and the peak wave period ΔTp for both WW3/ACM2 (Figs. 19a,b) and WW3/EC3 (Figs. 19c,d). Both parameters show projections of increasing wave period in the Southern Hemisphere and decreasing trends in the Northern Hemisphere. This is largely consistent with the trends seen in Hs (Fig. 17). The changes in the mean period (Figs. 19a,c), however, have a different spatial distribution than the changes in the peak period (Figs. 19b,d). In particular, the increase in the peak period Tp extends farther north into the Pacific ocean, and also impacts the Indian and the Atlantic oceans. This is connected to swell radiating from the increase in the Southern Ocean Hs (Fig. 17), a consequence of the increased intensity of the westerlies (Fig. 16). Again, the largest increase in the wind-wave periods is seen in the polar regions, impacted by the simultaneous increase in surface wind speed (Fig. 16) and the decrease in sea ice.

Fig. 19.
Fig. 19.

The percentage changes in (a),(c) mean Tm,02 and (b),(d) peak Tp wave period between two 30-yr slices: 1985–2014 and SSP5–8.5 2071–2100. (a),(b) WW3/ACM2 and (c),(d) WW3/EC3.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

d. Mean and peak direction

Small changes in wave direction could have major impacts on vulnerable coastlines and break their long-term erosion–accretion equilibrium (Harley et al. 2017). Figure 20 analyses the global normalized changes in mean wave direction Δθ¯ and peak wave direction Δθp from the WW3/ACM2 (Figs. 20a,b) and the WW3/EC3 (Figs. 20c,d) model results. In blue (red) we indicate a counterclockwise (clockwise) change in direction. Both θ¯ and θp are projected to turn counterclockwise in the ocean regions below 20°S. This is connected to the poleward shift of the Southern Ocean westerlies. Such changes extend to higher latitudes in the equatorial and tropical Pacific for the peak direction, again, as a consequence of the swells propagating from the storms in the high latitudes regions of the oceans. For the Northern Hemisphere high latitudes, the waves rotate clockwise again as a result of the poleward movement of the westerlies. Sharp changes in the wave direction contour plots in the tropics are a result of the changes in the trade wind intensity and location and the complicated equilibrium between different climatic systems contributing in these regions. Such changes in wave direction may have significant flood risk implications for already vulnerable low-lying islands (Hoeke et al. 2013) as well as for the geomorphology of coral reefs and atolls (Kench and Brander 2006; Kench et al. 2006).

Fig. 20.
Fig. 20.

Percentage changes between two 30-yr slices: 1985–2014 and SSP5–8.5 2071–2100 of (a),(c) mean wave direction θ¯ and (b),(d) peak wave direction θp. The black vectors plotted over the changes are the average directions for the 2071–2100 SSP5–8.5 scenario. Blue (red) color denotes a counterclockwise (clockwise) change in direction.

Citation: Journal of Climate 36, 6; 10.1175/JCLI-D-21-0929.1

8. Discussion and conclusions

This paper represents a comprehensive analysis of the wind-wave climate evolution across two centuries, from 1961 to 2100, as derived from a global wave model forced by ACCESS-CM2 and EC-Earth3 CMIP6 GCMs surface wind speed and sea ice concentration, under the SSP1–2.6 and SSP5–8.5 scenarios. The 140-yr wave climate dataset produced in this work significantly extends current state-of-the-art GCM-forced wave climate model datasets (Morim et al. 2019), updating the wind and sea ice forcing to the latest CMIP6 GCMs, and introducing long-term continuous wave climate simulations for climate variability analyses.

The datasets produced were extensively evaluated over the 1985–2014 historical period against reference observational datasets: A multimission satellite altimeter dataset (Ribal and Young 2019), long-term NDBC buoy observations, a state-of-the-art global hindcast (Liu et al. 2021), and the latest European reanalysis ERA5 (Hersbach et al. 2020). We found that the present CMIP6 GCM-forced wave models reproduce well the historical climate signal, and show greater skill in reproducing the historical wave climate than earlier CMIP phases GCM-forced wave models (Morim et al. 2020b). Significant biases still remain in the Northern Hemisphere midlatitude ocean regions where the positively biased GCMs surface wind speeds (Figs. 3b,c,e,f) generate larger waves in comparison with satellite observations over the 1985–2014 period (Figs. 4b,c,e,f). These biases are arguably related to an equatorward bias of the GCMs representation of storm tracks (Priestley et al. 2020; Harvey et al. 2020).

The largest uncertainties are found in the polar regions where the wind-wave climate is strongly impacted by the performance of the GCMs representation of sea ice (Roach et al. 2020). The sea ice extent influence may extend to most of the Southern Hemisphere wave climate, as the waves generated at the high latitudes propagate north across the ocean in the form of swells covering thousands of kilometers (Snodgrass et al. 1966; Young 1999). In this regard, the present wave model three-grid setup is optimal to perform computationally efficient simulations and assess the influence of sea ice GCMs representation on the Southern Hemisphere surface wave climate.

The present work also provides estimates of future wind-wave climate conditions through a seasonal Mann-Kendall trend analysis on the 140-yr simulated time series, and traditional time slice analyses. The 140-yr long-term continuous trends in global wind-wave climate appear to yield robust statistical results and improved statistical confidence. The long-term regional trends computed for the Iturbide et al. (2020) IPCC climatic regions provide an analysis of the wind-wave climate evolution for different regions of the global oceans and illustrate four regions of the oceans that are the most affected by human-induced climate change: the Southern Ocean, the North Atlantic, the North Pacific, and the Arctic Ocean. The changes found in these regions are in accordance with previous CMIP phases wave climate studies (Hemer et al. 2013; Morim et al. 2019; Casas-Prat and Wang 2020).

Following the results of a sensitivity analysis on the changes of significant wave height climate by the end of the twenty-first century (Fig. S18), we found that a 30-yr time slice is sufficient to satisfactorily remove the impact of interdecadal oscillations and ultimately perform a traditional time slice analysis. The time slice analysis confirmed the general pattern of change found by the long-term trends (Fig. 13), and allowed us to estimate the pattern of change for a number of the wind-wave parameter model outputs. By the end of the twenty-first century, the wave models project a distributed increase in significant wave height and wave period in the Southern Hemisphere, a consequence of the projected intensification and poleward movement of the westerlies (Goyal et al. 2021). As the westerlies are projected to shift poleward, the mean wave direction in the Southern Hemisphere is projected to change, with a counterclockwise change found in both WW3/ACM2 and WW3/EC3 projections (Fig. 20). Large uncertainties still characterize estimates of change in direction of large swell generated by storms. In the Northern Hemisphere, the significant wave height is projected to decrease by the end of the twenty-first century (Fig. 17). The analysis of the significant wave height probability distributions at selected locations in the Northern Hemisphere project a reduction in wave height variance, in parallel with a general reduction in the Hs magnitude. Additional research is needed to understand if these changes are consistent also at the extremes. In this regard, the present 3-hourly model outputs are a particularly attractive dataset as it allows applications of Extreme Value Analysis on unprecedentedly long-term datasets.

The continuous 140-yr wind-wave climate simulations proved valuable in assessing the climate variability impacts on the global wave climate. Future studies should use such long-term wind-wave climate datasets to further evaluate the interdecadal oscillation impacts in different regions of the oceans. The wave model outputs consist of 10 different integral parameters (Table 4), and global directional spectra, which have numerous practical applications. For instance, the wave direction, the wave period and the wave energy fluxes are important for both coastal safety and offshore marine structures and operations (Ochi 2005; Davidson-Arnott et al. 2019). In addition, the directional spectra not only enable an in-detail reconstruction of the wind-wave climate and its variability, but also serve as possible boundary conditions for future regional studies. Future wind-wave climate simulations should include a number of different integral parameters (as in Table 4) as well as globally distributed directional spectra.

In conclusion, this work contributes to the state-of-the-art of wind-wave climate studies with an updated and novel in-depth analysis of the wave climate across two centuries. The biases in the GCMs representation of wind speed and sea ice concentration still dominate the biases found in the performance of the wave climate models. However, the new CMIP6 GCM-forced wave models showed a clear improvement over the previous CMIP phases and justify the production of an eight-model ensemble of CMIP6 GCM-forced wind-wave climate models which is currently ongoing. These models will be part of an international collection of CMIP6 derived wave climate models, that will improve our understanding of the global oceans wind-wave climate and its future projections.

Acknowledgments.

We wish to thank Dr Qingxiang Liu, University of Melbourne for his advice on WW3 modelling and Dr. Jean Bidlot, ECMWF for his review of results. The M skill score software was developed by Ian G. Watterson in collaboration with Roger Bodman and Michael Grose of CSIRO. We wish also to thank Dr. Ghyslaine Boschat, Bureau of Meteorology, Australia, for the calculation of the SAM index. This project was supported by the Australian Research Council through grant DP210100840 and the Victorian Coastal Monitoring Program with funding through the Department of Environment, Land, Water and Planning. The computational resources were provided by the Australian National Computational Resource (NCI) through an NCMAS computational time grant. MH and CT were supported by the National Environmental Science Program Climate Systems Hub.

Data availability statement.

All the wave model data created during this study are openly available at http://hdl.handle.net/102.100.100/432508?index=1. The wind and sea ice data used as input for the wave model were downloaded from an NCI data repository, but are also openly available on the ESGF node at https://esgf-node.llnl.gov/search/cmip6/. The satellite altimeter data can be accessed directly at http://thredds.aodn.org.au/thredds/catalog/IMOS/SRS/Surface-Waves/Wave-Wind-Altimetry-DM00/catalog.html as cited in Ribal and Young (2019).

REFERENCES

  • Aarnes, O. J., S. Abdalla, J.-R. Bidlot, and Ø. Breivik, 2015: Marine wind and wave height trends at different ERA-interim forecast ranges. J. Climate, 28, 819837, https://doi.org/10.1175/JCLI-D-14-00470.1.

    • Search Google Scholar
    • Export Citation
  • Amores, A., and M. Marcos, 2020: Ocean swells along the global coastlines and their climate projections for the twenty-first century. J. Climate, 33, 185199, https://doi.org/10.1175/JCLI-D-19-0216.1.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., I. R. Young, and M. L. Banner, 2001: Breaking probabilities for dominant surface waves on water of finite constant depth. J. Geophys. Res., 106, 11 65911 676, https://doi.org/10.1029/2000JC000215.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., M. L. Banner, I. R. Young, and M. A. Donelan, 2007: Wave-follower field measurements of the wind-input spectral function. Part III: Parameterization of the wind-input enhancement due to wave breaking. J. Phys. Oceanogr., 37, 27642775, https://doi.org/10.1175/2007JPO3757.1.

    • Search Google Scholar
    • Export Citation
  • Bi, D., and Coauthors, 2020: Configuration and spin-up of ACCESS-CM2, the new generation Australian Community Climate and Earth System Simulator Coupled Model. J. South. Hemisphere Earth Syst. Sci., 70, 225251, https://doi.org/10.1071/ES19040.

    • Search Google Scholar
    • Export Citation
  • Boucher, O., and Coauthors, 2020: Presentation and evaluation of the IPSL-CM6A-LR climate model. J. Adv. Model. Earth Syst., 12, e2019MS002010, https://doi.org/10.1029/2019MS002010.

    • Search Google Scholar
    • Export Citation
  • Bugnot, A. B., and Coauthors, 2021: Current and projected global extent of marine built structures. Nat. Sustainability, 4, 3341, https://doi.org/10.1038/s41893-020-00595-1.

    • Search Google Scholar
    • Export Citation
  • Camus, P., I. Losada, C. Izaguirre, A. Espejo, M. Menéndez, and J. Pérez, 2017: Statistical wave climate projections for coastal impact assessments. Earth’s Future, 5, 918933, https://doi.org/10.1002/2017EF000609.

    • Search Google Scholar
    • Export Citation
  • Casas-Prat, M., and X. L. Wang, 2020: Projections of extreme ocean waves in the Arctic and potential implications for coastal inundation and erosion. J. Geophys. Res. Oceans, 125, e2019JC015745, https://doi.org/10.1029/2019JC015745.

    • Search Google Scholar
    • Export Citation
  • Casas-Prat, M., X. L. Wang, and N. Swart, 2018: CMIP5-based global wave climate projections including the entire Arctic Ocean. Ocean Modell., 123, 6685, https://doi.org/10.1016/j.ocemod.2017.12.003.

    • Search Google Scholar
    • Export Citation
  • Chang, E. K. M., Y. Guo, and X. Xia, 2012: CMIP5 multimodel ensemble projection of storm track change under global warming. J. Geophys. Res., 117, D23118, https://doi.org/10.1029/2012JD018578.

    • Search Google Scholar
    • Export Citation
  • Collins, M., and Coauthors, 2019: Extremes, abrupt changes, and managing risk. Climate Change 2019: The Physical Science Basis, H. O. Pörtner et al., Eds., Cambridge University Press, 589–655.

  • Davidson-Arnott, R., B. Bauer, and C. Houser, 2019: Introduction to Coastal Processes and Geomorphology. Cambridge University Press, 536 pp.

  • Dodet, G., and Coauthors, 2020: The Sea state CCI dataset v1: Towards a sea state climate data record based on satellite observations. Earth Syst. Sci. Data, 12, 19291951, https://doi.org/10.5194/essd-12-1929-2020.

    • Search Google Scholar
    • Export Citation
  • Donelan, M. A., A. V. Babanin, I. R. Young, M. L. Banner, and C. McCormick, 2005: Wave-follower field measurements of the wind-input spectral function. Part I: Measurements and calibrations. J. Atmos. Oceanic Technol., 22, 799813, https://doi.org/10.1175/JTECH1725.1.

    • Search Google Scholar
    • Export Citation
  • Donelan, M. A., A. V. Babanin, I. R. Young, and M. L. Banner, 2006: Wave-follower field measurements of the wind-input spectral function. Part II: Parameterization of the wind input. J. Phys. Oceanogr., 36, 16721689, https://doi.org/10.1175/JPO2933.1.

    • Search Google Scholar
    • Export Citation
  • Döscher, R., and Coauthors, 2022: The EC-Earth3 Earth system model for the Coupled Model Intercomparison Project 6. Geosci. Model Dev., 15, 29733020, https://doi.org/10.5194/gmd-15-2973-2022.

    • Search Google Scholar
    • Export Citation
  • Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 19371958, https://doi.org/10.5194/gmd-9-1937-2016.

    • Search Google Scholar
    • Export Citation
  • Fox-Kemper, B., and Coauthors, 2021: Ocean, cryosphere and sea level change. Climate Change 2021: The Physical Science Basis, V. Masson-Delmotte et al. Eds., Cambridge University Press, 1211–1361.

  • Gong, D., and S. Wang, 1999: Definition of Antarctic oscillation index. Geophys. Res. Lett., 26, 459462, https://doi.org/10.1029/1999GL900003.

    • Search Google Scholar
    • Export Citation
  • Goyal, R., A. Sen Gupta, M. Jucker, and M. H. England, 2021: Historical and projected changes in the Southern Hemisphere surface westerlies. Geophys. Res. Lett., 48, e2020GL090849, https://doi.org/10.1029/2020GL090849.

    • Search Google Scholar
    • Export Citation
  • Grigorieva, V. G., S. K. Gulev, and A. V. Gavrikov, 2017: Global historical archive of wind waves based on voluntary observing ship data. Oceanology, 57, 229231, https://doi.org/10.1134/S0001437017020060.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., and V. Grigorieva, 2004: Last century changes in ocean wind wave height from global visual wave data. Geophys. Res. Lett., 31, L24302, https://doi.org/10.1029/2004GL021040.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., and V. Grigorieva, 2006: Variability of the winter wind waves and swell in the North Atlantic and North Pacific as revealed by the voluntary observing ship data. J. Climate, 19, 56675685, https://doi.org/10.1175/JCLI3936.1.

    • Search Google Scholar
    • Export Citation
  • Harley, M. D., and Coauthors, 2017: Extreme coastal erosion enhanced by anomalous extratropical storm wave direction. Sci. Rep., 7, 6033, https://doi.org/10.1038/s41598-017-05792-1.

    • Search Google Scholar
    • Export Citation
  • Harvey, B. J., P. Cook, L. C. Shaffrey, and R. Schiemann, 2020: The response of the Northern Hemisphere storm tracks and jet streams to climate change in the CMIP3, CMIP5, and CMIP6 climate models. J. Geophys. Res. Atmos., 125, e2020JD032701, https://doi.org/10.1029/2020JD032701.

    • Search Google Scholar
    • Export Citation
  • Hausfather, Z., and G. P. Peters, 2020: Emissions—The ‘business as usual’ story is misleading. Nature, 577, 618620, https://doi.org/10.1038/d41586-020-00177-3.

    • Search Google Scholar
    • Export Citation
  • Hemer, M. A., and C. E. Trenham, 2016: Evaluation of a CMIP5 derived dynamical global wind wave climate model ensemble. Ocean Modell., 103, 190203, https://doi.org/10.1016/j.ocemod.2015.10.009.

    • Search Google Scholar
    • Export Citation
  • Hemer, M. A., J. A. Church, and J. R. Hunter, 2010: Variability and trends in the directional wave climate of the Southern Hemisphere. Int. J. Climatol., 30, 475491, https://doi.org/10.1002/joc.1900.

    • Search Google Scholar
    • Export Citation
  • Hemer, M. A., X. L. Wang, R. Weisse, and V. R. Swail, 2012: Advancing wind-waves climate science: The COWCLIP project. Bull. Amer. Meteor. Soc., 93, 791796, https://doi.org/10.1175/BAMS-D-11-00184.1.

    • Search Google Scholar
    • Export Citation
  • Hemer, M. A., Y. Fan, N. Mori, A. Semedo, and X. L. Wang, 2013: Projected changes in wave climate from a multi-model ensemble. Nat. Climate Change, 3, 471476, https://doi.org/10.1038/nclimate1791.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Hinkel, J., and Coauthors, 2014: Coastal flood damage and adaptation costs under 21st century sea-level rise. Proc. Natl. Acad. Sci. USA, 111, 32923297, https://doi.org/10.1073/pnas.1222469111.

    • Search Google Scholar
    • Export Citation
  • Hinkel, J., and Coauthors, 2021: Uncertainty and bias in global to regional scale assessments of current and future coastal flood risk. Earth’s Future, 9, e2020EF001882, https://doi.org/10.1029/2020EF001882.

    • Search Google Scholar
    • Export Citation
  • Hirsch, R. M., and J. R. Slack, 1984: A nonparametric trend test for seasonal data with serial dependence. Water Resour. Res., 20, 727732, https://doi.org/10.1029/WR020i006p00727.

    • Search Google Scholar
    • Export Citation
  • Hirsch, R. M., J. R. Slack, and R. A. Smith, 1982: Techniques of trend analysis for monthly water quality data. Water Resour. Res., 18, 107121, https://doi.org/10.1029/WR018i001p00107.

    • Search Google Scholar
    • Export Citation
  • Hoeke, R. K., K. L. McInnes, J. C. Kruger, R. J. McNaught, J. R. Hunter, and S. G. Smithers, 2013: Widespread inundation of Pacific islands triggered by distant-source wind-waves. Global Planet. Change, 108, 128138, https://doi.org/10.1016/j.gloplacha.2013.06.006.

    • Search Google Scholar
    • Export Citation
  • Holthuijsen, L. H., 2010: Waves in Oceanic and Coastal Waters. Cambridge University Press, 404 pp.

  • Hwang, P. A., 2011: A note on the ocean surface roughness spectrum. J. Atmos. Oceanic Technol., 28, 436443, https://doi.org/10.1175/2010JTECHO812.1.

    • Search Google Scholar
    • Export Citation
  • Iturbide, M., and Coauthors, 2020: An update of IPCC climate reference regions for subcontinental analysis of climate model data: Definition and aggregated datasets. Earth Syst. Sci. Data, 12, 29592970, https://doi.org/10.5194/essd-12-2959-2020.

    • Search Google Scholar
    • Export Citation
  • Kench, P. S., and R. W. Brander, 2006: Wave processes on coral reef flats: Implications for reef geomorphology using Australian case studies. J. Coastal Res., 221, 209223, https://doi.org/10.2112/05A-0016.1.

    • Search Google Scholar
    • Export Citation
  • Kench, P. S., R. W. Brander, K. E. Parnell, and R. F. McLean, 2006: Wave energy gradients across a Maldivian atoll: Implications for island geomorphology. Geomorphology, 81, 117, https://doi.org/10.1016/j.geomorph.2006.03.003.

    • Search Google Scholar
    • Export Citation
  • Kirezci, E., I. R. Young, R. Ranasinghe, S. Muis, R. J. Nicholls, D. Lincke, and J. Hinkel, 2020: Projections of global-scale extreme sea levels and resulting episodic coastal flooding over the 21st century. Sci. Rep., 10, 11629, https://doi.org/10.1038/s41598-020-67736-6.

    • Search Google Scholar
    • Export Citation
  • Kumar, P., S.-K. Min, E. Weller, H. Lee, and X. L. Wang, 2016: Influence of climate variability on extreme ocean surface wave heights assessed from ERA-Interim and ERA-20C. J. Climate, 29, 40314046, https://doi.org/10.1175/JCLI-D-15-0580.1.