Influence of natural climate variability on extreme wave power over Indo-Pacific Ocean assessed using ERA5

In recent decades, wave power (WP) energy from the ocean is one of the cleanest renewable energy sources associated with oceanic warming. In Indo-Pacific Ocean, the WP is significantly influenced by natural climate variabilities, such as El Niño Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and Pacific Decadal Oscillation (PDO). In this study, the impact of major climate variability modes on seasonal extreme WP is examined over the period 1979–2019 using ERA5 reanalysis data and the non-stationary generalized extreme value analysis is applied to estimate the climatic extremes. Independent ENSO influence after removing the IOD impact (ENSO|IOD) on WP are evident over the northeast and central Pacific during December–February, and March–May, respectively, which subsequently shifts towards the western Pacific in June–August (JJA) and September–November (SON). The ENSO|PDO impact on WP exhibits similar yet weaker intensity year round compared to ENSO. Extreme WP responses due to the IOD|ENSO include widespread decreases over the tropical and eastern Indian Ocean, with localized increases only over South China and Philippine seas and Bay of Bengal during JJA, and the Arabian Sea during SON. Lastly, for the PDO|ENSO, the significant increases in WP are mostly confined to the Pacific, and most prominent in the North Pacific. Composite analysis of different phase combinations of PDO (IOD) with El Niño (La Niña) reveals stronger (weaker) influences year-round. The response patterns in significant wave height, peak wave period, sea surface temperatures, and sea level pressure help to explain the seasonal variations in WP.


Introduction
The depletion of conventional energy resources and increasing global warming due to the consumption of fossil fuels have prompted interest in renewable energy resources in many countries (Cornett 2008). Among the various renewable energy resources such as wind, solar, hydro-power, etc., wave power is one of the most important and least studied renewable energy resources. Recent studies suggest that the spatial and temporal variations in wave power are induced by natural climate variabilities like El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multidecadal Oscillation (AMO) (Bromirski and Cayan 2015;Bromirski et al. 2013;Reguero et al. 2019;Yang and Oh 2020). Therefore, a better comprehension of wave power and its relation to natural climate variability is essential for social and economic development.
Wave Power (WP), which measures the transport of energy that is transmitted by air-to-sea exchanges and used for wave propagation (Donelan et al. 1997;Reguero et al. 2019), depends not only on wave height but also on wave period. Moreover, WP represents the accumulated wave energy over periods such as months, seasons, and years, unlike other wave climate parameters e.g., significant wave height (SWH) that must be averaged (Reguero et al. 2019). Therefore, WP is more informative than measuring wave height alone for assessing coastal vulnerability. For example, a large wave period produces high wave run-up, resulting in large suspended sediment transport, coastal erosion, increase flooding potential, etc. (Bromirskiet al. 2012(Bromirskiet al. , 2013. Coastal inundation depends on both wave height and wave period, so, assessing the fluctuations and trends in WP, which better describes the long-term behavior of wave climate than wave height, is crucial. However, previous studies predominately emphasized the historical trends in wind and wave climates at the global (Caires et al. 2006;Meucci et al. 2020;Reguero et al. 2012;Stopa et al. 2013;Young et al. 2011Young et al. , 2012; Young and Ribal2019) and regional scale (Allan and Komar 2006;Gulev and Grigorieva 2006;Hemer et al. 2008Hemer et al. , 2010Menendez et al. 2008;Swail 2001, 2006;Wang et al. 2009. In addition, other wave climate indicators, such as wave period and/or direction, have also been investigated extensively to identify underlying properties in the changes to mean and extreme SWH (Chen et al. 2002;Semedo et al. 2011;Sterl and Caires 2005;Young 1999;Zhang et al. 2011;Zheng et al. 2016).
In the context of WP, several studies have previously analyzed the monthly and annual variations in mean wave power at the global scale (Arinaga and Cheung 2012;Barstow et al. 2008;Cornett 2008;Gunn and Stock-Williams 2012;Hulls 1977;Mollison 1986;Mork et al. 2010). Further, the seasonal variations in mean wave power were examined by Mackay (2012). However, these analyses were conducted based on either satellite data or wave models such as Wave Watch-III (WW3) and ECMWF WAM for relatively short periods of 6 or 10 or 12 years. Long-term seasonal and interannual variations in global mean wave power were investigated by Reguero et al (2015) using WW3 data for 61 years . In this regard, numerous regional studies have also been conducted. For example, the North Pacific (NP) (Bromirski et al. 2005(Bromirski et al. , 2013Yang and Oh 2020), North Atlantic (NA) (Bromirski and Kossin 2008;Bromirski and Cayan 2015;Santo et al. 2015), Black Sea (Aydogan et al. 2013), along the Australian coasts (Hemer et al. 2016, and shelf seas of India (Kumar and Anoop 2015;Sannasiraj and Sundar 2016;Amrutha et al. 2019;Amrutha and Kumar 2020). However, seasonal/annual variations in extreme WP have not been assessed yet at the global and regional scales.
Although many studies have focused on seasonal/annual variations in mean WP as described above, the natural climate variabilities such as the ENSO, Indian Ocean Dipole (IOD), and PDO, etc. can exert a significant impact on wave climate through large-scale atmospheric circulation patterns with different seasonal and regional features (Hemer et al. 2010;Izaguirre et al. 2010Izaguirre et al. , 2011Kumar et al 2016Kumar et al , 2019Marshall et al. 2018;Menéndez et al. 2008;Patra et al. 2020;Wandres et al. 2018;Yang and Oh 2018). However, influences due to such large-scale natural climate variability modes on WP remain unclear, except for limited regional and global-scale studies. For example, using the WW3 wave model for the period 1948-2008, the PDO influence on WP across the NP region was investigated by Bromirski et al. (2013) and NAO influence on WP across the NA region by Bromirski and Cayan (2015) during winter (November-March) and summer (May-September). Recently, Yang and Oh (2020) examined the effect of ENSO and PDO on WP during boreal summer (June-August, JJA) in the western NP. At the global scale, Reguero et al. (2015) analyzed the interrelation between the annual mean WP and fifteen climate variability modes, which include ENSO, IOD, and PDO. Recently, the ENSO and AMO influence on annual mean WP have been reported by Reguero et al. (2019). Such studies were predominantly concerned with the seasonal/annual impact of natural climate variability on mean WP.
"Extreme" events are significant departures from the normal climate state and often have widespread societal and ecological impacts. The changes in extreme and mean wave characteristics have been reported to be different Mori et al. 2010), and are observed to be linked with more frequent extreme events. Therefore, it is crucial to analyze the influence of natural climate variability on extreme parameters, which exert stronger impacts than mean. Further, the simple linear regression analysis is used for mean variables and cannot be applied to extreme variables because of their non-normality nature (Coles 2001), and recent studies have widely used the extreme value theory to investigate the impact of climate variability on extreme parameters such as SWH, wind, wave period, etc. (Izaguirre et al. 2010(Izaguirre et al. , 2011Kharin and Zwiers 2005;Kumar et al 2016Kumar et al , 2019Menéndez et al. 2008;Min et al. 2013;Patra et al. 2020;Zhang et al. 2010). Despite this, no previous study assessed the impact of natural climate variability on extreme WP, particularly in the Indo-Pacific Ocean.
This study investigates the seasonal influence of dominant modes of natural climate variability, namely the ENSO, IOD, and PDO, on extreme WP in the Indo-Pacific Ocean using ERA5 reanalysis data for the 41 years from 1979 to 2019. For this purpose, firstly, the four boreal seasons (i.e., December-February (DJF, winter), March-May (MAM, spring), June-August (JJA, summer), and September-November (SON, autumn)) are considered to understand the seasonal influence of natural climate variability on extreme WP and a non-stationary generalized extreme value (GEV) analysis (Kharin and Zwiers 2005;Zhang et al. 2010;Min et al. 2013) is applied to determine/capture the seasonal extremes. Regions with statistically significant responses at the 5% level are marked by hatch lines. In addition, the seasonal influence of natural climate variability on extreme SWH, Peak Wave Period (PWP), and wind speed is also investigated to explore the associated underlying mechanisms in enhancing or reducing the WP in the Indo-Pacific Ocean as WP comprises information about SWH and PWP. The seasonal teleconnection patterns of WP and SWH are explained through/by sea level pressure (SLP) and sea surface temperature (SST). Overall, large sea-level variations (driven by anomalous high or low-pressure systems) are generally associated with warm/cool SSTs, which in turn produce strong winds and consequently enhance the wave parameters (i.e. wave height and period) (Kumar et al. 2016Patra et al. 2020).
As different modes of natural climate variability tend to interact with each other in specific seasons (Cai et al. 2011;Kumar et al. 2016Kumar et al. , 2019. Therefore, an independent analysis of seasonal mean and extreme WP, SWH, PWP, and wind speed is carried out to assess the role of one variability mode in strengthening and weakening the other variability mode influence in different seasons. Additionally, the composite analysis of mean and extreme WP for the different phase combinations of natural climate variabilities (i.e. ENSO, IOD, and PDO) is also conducted to get further insight into the inter-relation between different variability modes. The novelty of the current study in comparison to previous relevant studies is detailed in Table 1.
The remainder of the paper is structured as follows. Data and methodology are detailed in Sect. 2 and teleconnection patterns in Sect. 3. Section 4 provides a detailed investigation of the influence of natural climate modes (in particular the ENSO, IOD, and PDO) and their impendent impact on seasonal mean and extreme WP, SWH, and PWP. Composite analysis for different phase combinations of ENSO with IOD and ENSO with PDO is presented in Sect. 5. Section 6 provides a summary and conclusions.

Data
The latest reanalysis product from the European Centre for Medium-Range Weather Forecasting (ECMWF), referred to as the ERA5 reanalysis (Hersbach and Dee 2016), is used in the present study to analyze the mean and extreme WP for the 41-year period from 1979 to 2019 over the Indo-Pacific region for the four boreal seasons (i.e., December-February (DJF, winter), March-May (MAM, spring), June-August (JJA, summer), and September-November (SON, autumn)). The ERA5 reanalysis is produced by using the Integrated Forecast System (IFS) Cycle 41r2 with 4D-Var data assimilation, as released in 2016. The horizontal resolution of the ERA5 data set is ~ 31 km (T L 639 spectral grid) on 137 hybrid sigma/pressure (model) vertical levels, with the toplevel located at 0.01 hPa (about 80 km of altitude). Additionally, hourly estimates of a vast/large number of atmospheric, land, and oceanic climate variables are also provided by ERA5. The ERA5 reanalysis data have several advancements compared to its predecessor, ERA-Interim (Dee et al. 2011). In contrast to ERA-Interim, ERA5 has higher spatial and temporal resolution along with an improved representation of the tropospheric processes, including better representation of tropical cyclones, zglobal balance of precipitation and evaporation cycle, etc. In order to measure the WP, the seasonal mean and maxima of SWH (of combined wind waves and swell) and PWP are obtained from the six-hourly SWH and PWP data taken from ERA5. The seasonal mean and extreme wind speed data are also calculated from the 6-hourly wind data of ERA5. Similarly, the seasonal mean SLP and SST were also derived from 6-hourly SLP and SST data of ERA-5, respectively. In this study, the ERA5 reanalysis data for all the variables were downloaded from the ECMWF website (https:// www. ecmwf. int/ en/ forec asts/ datas ets/ reana lysis-datas ets/ era5/) at a horizontal resolution of 0.5° × 0.5° (i.e. SWH, wind speed, and PWP) or 0.25° × 0.25° (i.e., SST and SLP).

Climate indices
Indices used to represent climate variability associated with ENSO, IOD, and PDO over 1979-2019 were obtained from several online sources. Overall, ENSO is the dominant coupled ocean-atmosphere interaction occurring over the equatorial Pacific and significantly affects the interannual climate variability globally (Collins et al. 2010;Stevenson 2012). In order to examine the seasonal ENSO influence, the Niño-3.4 index (referred to as N34 herein) which represents the average SST anomalies over the equatorial eastern Pacific (5° N-5° S, 170° W-120° W) was obtained from the National Oceanic and Atmospheric Administration/Climate Prediction Center http:// www. cpc. ncep. noaa. gov/ data/ indic es/). To quantify the IOD impact, the dipole mode index (DMI) was used (Saji et al. 1999;Webster et al. 1999), which is a measure of the difference between the area-averaged SST anomalies in the western tropical Indian Ocean (TIO) (50°-70° E, 10° S-10° N) and southeastern TIO (90°-110° E, 10° S-Equator). Monthly SST anomalies were acquired from the Extended Reconstructed Sea Surface Temperature (ERSST) dataset to calculate the seasonal DMI index. The PDO index, prescribed as the principal mode of NP monthly SST anomalies poleward of 20° N (Zhang et al. 1997), was obtained from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) at the University of Washington (http:// resea rch. jisao. washi ngton. edu/ pdo/). Natural climate variability modes can interact with each other during different seasons (Cai et al. 2011). Consequently, the independent influence of each should be considered when assessing the impact of each model. The seasonal correlation coefficients between the detrended N34 and DMI, and N34 and PDO indices are shown in Table 2 for the period1979-2019. A significant positive correlation (at the 1% level) between the N34 and PDO index is found during all seasons, with a range of 0.397-0.545. ForN34 and DMI indices, positive correlations only occur during JJA (i.e.0.312, p-value < 0.05) and SON (0.620, p-value < 0.01). The significant correlation between ENSO and IOD in JJA and SON suggests that IOD can be largely determined by ENSO and seasonally modulated responses, yet some IOD events can occur independently of ENSO events (Cai et al. 2011;Kumar et al. 2019;Stucker et al. 2017). When analyzing the independent impact of each climate variability mode, the dependency of one climate variability index on the other is removed using linear regression analysis. For example, ENSO| IOD denotes the linearly independent residual ENSO index obtained after the removal of IOD from ENSO.

Wave Power (WP)
In essence, WP measures the transmission of energy by/ through air-sea exchanges and is used for wave motion (Donelan et al. 1997), is expressed as follows (Cornett 2008;Yang and Oh 2020): where g denotes the acceleration due to gravity, ρ is the seawater mass density (~ 1028 kg/m 3 ), Hs is the SWH, and T e is the energy period. The energy period is estimated from the spectral shape and other parameters. When PWP (T p ) is known, the energy period is estimated by using the following relation (Cornett 2008): where α depends on the shape of the wave spectrum and increases towards unity with decreasing spectral width. Hagerman (2001) assumed T e = T p in the assessment of the wave energy resources over southern New England. In this study, the same assumption is adopted. On substituting T e = T p into Eq. (1), WP is expressed as:

Generalized Extreme Value (GEV) distribution
Climate extremes are significant departures from the normal climate state and often have widespread societal and ecological impacts. Thus, the correct representation of extreme events is essential to understand their impacts. Extreme value theory provides the statistical description of extremes in stationary and non-stationary processes. However, in the context of environmental variables (e.g., SWH, temperature, precipitation), a non-stationary variable is used (Coles and Casson 1999;Gellens 2002;Nogaj et al. 2007;Zwiers 2000, 2005), whereby extreme events are defined by three extreme value distributions, i.e., Gumbel distribution, Fréchet distribution, or Weibull distribution, arising from the limiting theorem of Fisher and Tippett (1928). The three distributions can be combined into a single form, the nonstationary GEV distribution, and its cumulative distribution function is given as: where −∞ < t < ∞, t > 0, and − ∞ < t < ∞ represent the location, scale, and shape parameters, respectively. For the non-stationary GEV distribution, the climate variability t (here, IOD, ENSO, and PDO indices, which are detrended and normalized) that varies with time (t) is used as a covariate of the GEV parameters. The location parameter ( t ) as a function of climate variability is written as: (2) T e = T p , where 0 represents the location parameter at time t 0 , and 1 denotes the regression coefficient representing the relationship between the climate variable and location parameter. Additionally, the scale and shape parameters can also be expressed as a function of climate variability as follows: where σ 0 and ξ 0 are the scale and shape parameter values at time t 0 , respectively, and σ 1 and 1 are the corresponding regression coefficients. In order to examine the statistical significance of climate variability on extremes, the log-likelihood ratio test is used. The log-likelihood test compares the non-stationary GEV model with the stationary GEV model and assesses the GEV parameters (Kharin and Zwiers 2005;Zhang et al. 2010).

SST and SLP mean teleconnection
The patterns of seasonal mean SST and SLP regressed onto ENSO| IOD , IOD| ENSO , ENSO| PDO , and PDO| ENSO over the period 1979-2019 is shown in Fig. 1, and regions with statistically significant responses at the 5% level are indicated by hatching. A similar analysis for wind speed is also provided in Supplementary Fig. 1. Significant canonical responses in SST to ENSO| IOD are evident over the eastern PO (warmer conditions during El Niño) and western PO (colder conditions) throughout the year. In the Indian Ocean (IO), the strongest signals in SST are found over the majority of the North Indian Ocean (NIO) and TIO in DJF and MAM, NIO in JJA, and NIO and western TIO in SON (Fig. 1a). Further, the ENSO| IOD influence on SLP shows high and low-pressure anomalies in eastern and western regions of the southern Indo-Pacific Ocean, respectively, during DJF. This anomalous pressure pattern generates strong winds over the southern Indo-Pacific Ocean, leading to an enhancement in both SWH and PWP in DJF (Fig. 1b). Similarly, the Southern Oscillation pattern of the coupled high and low-pressure anomalies is also seen in DJF over the western and eastern PO, respectively. This too presumably leads to both strong winds and enhances the wave parameters (i.e., SWH and PWP) over the eastern PO (Fig. 1b), consistent with previous findings (Kumar et al. 2016;Patra et al. 2020). With the progression of the seasons from DJF through to SON, the high and low-pressure anomalies shift from the western PO and eastern PO, respectively, to the central-western PO and eastern PO during JJA (Yang and Oh 2020), and further to the western PO and central-eastern PO, respectively, during SON. Additionally, high-pressure anomalies are observed over the NIO, TIO, and eastern parts of the SO, with lowpressure anomalies over the central parts of the SO during MAM, JJA, and SON. Such strong responses associated with SLP changes will also lead to strong responses in the winds and wave parameters (Fig. 1b).
Significant impacts of IOD| ENSO on SST are predominantly confined to the western IO and Arabian Sea (AS) in DJF, which extend into parts of the tropical Pacific in MAM. During JJA and SON, the IOD| ENSO is associated with positive SST anomalies over the western-to-central IO (Fig. 1a). The corresponding responses in SLP during DJF show highpressure anomalies over most of the tropical and mid-latitude region of the Indo-Pacific Ocean, and low-pressure anomalies over the AS and high-latitude region of the Indo-Pacific Ocean. In MAM, the IOD| ENSO influence is most significant over the mid-to-high latitudes in both hemispheres. In JJA, high SLP anomalies expand over the mid-latitudes of the Indo-Pacific Ocean, from the eastern IO to central PO, and low-pressure anomalies strengthen and expand over the western IO. In SON, high SLP anomalies are evident over the eastern IO and tropical PO, and develop over the eastern southern PO, whereas the low-pressure anomalies over the western IO are similar to JJA. Such high and low SLP anomalies, with progressing seasonal patterns, will consequently produce strong winds and consequently enhance the wave parameters in the respective regions (Fig. 1b).
The ENSO| PDO impact closely resembles that of ENSO| IOD whereby warmer SSTs are evident over the eastern PO and colder SST over the western PO year around (c.f. first and third rows in Fig. 1a). In the IO, significant positive signals in SST due to ENSO| PDO are again evident over large parts of the NIO and TIO in most seasons, being weakest in JJA (Fig. 1a). Further, the ENSO| PDO influence on SLP is also consistent with that of ENSO| IOD whereby the significant signals being associated with the widespread high and low-pressure anomalies over the western and eastern Indo-Pacific Ocean, respectively (c.f. first and third rows in Fig. 1b). However, high-pressure anomalies are subdued in the western IO during SON for ENSO| PDO compared to that associated with ENSO| IOD . Thus, the above changes of both ENSO| IOD and ENSO| PDO are likely to generate similar variations in the generated winds and wave fields in the respective regions, except for the western IO in SON.
The independent PDO influence (i.e., PDO| ENSO ) on SST is observed to induce a consistent year-round pattern with long-term SST increases (warm SST) over the eastern PO (extending towards the west along the equator) and decreases (cold SST) over the western NP and southwest tropical PO (Fig. 1a). This represents the typical pattern associated with a positive PDO. In the IO, the strong PDO| ENSO influences on SST occur over the AS in MAM, NIO, and South China and Philippine (SCP) seas in JJA, and Bay of Bengal (BOB) and SCP seas in SON (Fig. 1a). A positive PDO (pPDO)-East Asian teleconnection also forces seasonal variations in the SST pattern over the IO (Girishkumar et al. 2015;Kim et al. 2014). The corresponding responses in SLP exhibit an anomalous low pressure over the north and tropical Pacific and an anomalous high pressure over the eastern TIO in DJF (Fig. 1b). In addition, anomalous high and low-pressure centers are evident over the south Pacific in DJF. In MAM, positive responses in SLP to the PDO| ENSO are observed over the large section of the tropical and mid-latitude region of the Indo-Pacific Ocean, with counter responses (low-pressure anomalies) over high latitudes of the Indo-Pacific Ocean. In JJA, the PDO| ENSO influence on SLP is most significant over the western Pacific Ocean (PO) (high-pressure anomalies) and eastern NP and Southern Ocean (SO) (low-pressure anomalies). These anomalies propagate into the western NP (high-pressure anomalies) and central NP (low-pressure anomalies) in SON. In SON, high and lowpressure anomalies are evident over the SO.

ENSO influence
Spatial patterns of the seasonal mean and extreme WP (WPavg and WPmax), SWH (Havg and Hmax), and PWP (Pavg and Pmax) responses to independent ENSO| IOD influence (i.e. the independent ENSO influence obtained after the removal of IOD signals) over the period 1979-2019 in the Indo-Pacific Ocean are shown in Fig. 2. In addition, the original seasonal ENSO influence (i.e., no removal of covarying IOD signals) on the mean and extreme WP, SWH, and PWP is also provided in Supplementary Fig. 2 to assess the role of IOD in strengthening and weakening the ENSO impact. Overall, mean responses in WPavg, Havg, and Pavg were acquired by using linear regression whereas extreme responses in WPmax, Hmax, and Pmax were based on the non-stationary GEV analysis. Regions with statistically significant responses at the 5% level are indicated by hatching. Widespread positive responses in WPmax to ENSO| IOD are evident over the central equatorial Pacific, northeastern North Pacific (NP), Intertropical Convergence Zone (ITCZ), South Pacific Convergence Zone (SPCZ), and southern part of the IO (an extension from south of Australia). However, counter-responses are evident over the coastal regions of western NP (WNP) and Maritime Continent (MC) in DJF (Fig. 2a). The similar regional variations in wind speed over these regions in DJF are evident, which are associated with the large-scale patterns in SLP/SST (Figs. 1 and 2, and Supplementary Fig. 1). The El Niño events enhance the extra-tropical wave climate in the northeast NP as the warm phase of ENSO is associated with a stronger Aleutian Low (Li et al. 2015), leading to intensified tropical cyclones (Jin et al. 2014). While, warmer (colder) ocean surface and reduced storm activities result in less intense WP extremes along the coast of western NP and Maritime Continent (Power et al. 1999;Wang et al. 2000). The increase in WPmax along the SPCZ region is correlated with enhanced tropical cyclone activities during El Niño (Kuleshov et al. 2008;Vincent et al. 2011). This is because increased, sustained wind speed is a major contributor to increased WPmax, which relates to anomalously high or low-pressure systems over the PO (c.f. Figs. 1 and 2, and Supplementary Fig. 1).
As the seasons progress from DJF through to SON, large seasonal variations in WP are observed in both the IO and PO. In the PO, positive amplitudes of the WPmax occur more over the central Pacific in MAM, which shifts further towards the western Pacific in JJA and SON (Fig. 2a). As during JJA, tropical cyclone activities in the WNP are reinforced by El Niño events, resulting in an increase in the WPmax over the WNP (Yang and Oh 2020). This is due to the fact that enhanced wind speeds, driven by anomalously high or low-pressure systems over the PO, during JJA are a dominant factor to intensify the WPmax over WNP (c.f. Figs. 1 and 2, and Supplementary Fig. 1). In SON, the strong increases in extreme WP over the WNP are associated with the deepening of the East Asian trough, as well as the intensification and more frequent northward shift of the storm tracks across WNP during El Niño (Wang and Zhang 2002). However, WPmax exhibits larger seasonality in the IO compared to the PO. For example, the WPmax increases over the western TIO in MAM, over the western TIO, AS, BOB, southern IO in JJA, and over the eastern TIO during SON in response to ENSO| IOD (Fig. 2a). In DJF, El Niño weakens the tropical Walker cell and trade winds (Reiter 1978), resulting in a debilitating wave climate over the TIO (Odériz et al. 2021) (Figs. 1 and 2, and Supplementary Fig. 1). In JJA, La Niña (a pattern that is opposite during El Niño) reinforces the WPmax of AS, due to the increase in the pressure gradient between the IO and East Pacific (Odériz et al. 2021;Wang et al. 2000;Wang and He 2012;Zhang et al. 1996) whereas, El Niño enhanced tropical cyclone activity in the BOB results in enhanced WPmax (Singh et al. 2001) (c.f. Figs. 1 and 2 and Supplementary Fig. 1). The regression patterns of ENSO| IOD on mean WP are similar to the extreme. Consistently, the ENSO| IOD influence on Havg and Hmax over the Indo-Pacific Ocean (Fig. 2b) shows similar seasonal and regional variations as WPavg and WPmax, due to SWH being a dominating factor in determining the WP (Bromirski et al. 2005(Bromirski et al. , 2013Reguero et al. 2019;Yang and Oh 2020). Lastly, the impact of ENSO| IOD on Pavg and Pmax is found to be largest over the eastern PO in DJF and over the western PO in JJA and SON (Fig. 2c). Such regions exhibit a significant relationship, whereby changes to tropical SST anomalies due to the warm ENSO phase resulted in variations in anomalous long PWP. In the IO, however, significant increases in Pavg and Pmax are observed over large parts of the IO year-round due to ENSO| IOD , but more so in DJF and MAM (Fig. 2c).
Comparing independent ENSO influences (ENSO| IOD ) to the original ENSO signals (c.f. Fig. 2 and Supplementary Fig. 2), an increase in WPmax and WPavg is evident over the eastern TIO in JJA and SON, and over the central NP in SON for the independent ENSO influence. This indicates that the IOD acts to reduce the ENSO impact in these regions during JJA and SON. In addition, a similar enhancement in the independent ENSO signal is also exhibited in the mean and extreme SWH responses when the covarying IOD signal is removed during JJA and SON (c.f. Fig. 2b and Supplementary Fig. 2b). However, positive responses in mean and extreme PWP associated with ENSO in the IO are significantly reduced during SON when the covarying IOD signal is removed (c.f. Fig. 2c and Supplementary  Fig. 2c). In DJF and MAM, the ENSO| IOD impact on mean and extreme WP, SWH, and PWP exhibits similar regional variations as observed for the complete ENSO signals as the IOD is not active during these seasons.

IOD influence
Seasonal spatial regression patterns of mean and extreme WP, SWH, and PWP against the independent IOD influence (denoted as IOD| ENSO ) after removing the ENSO signal over 1979-2019 in the Indo-Pacific Ocean are presented in Fig. 3. Further, the original seasonal IOD influence (here using the DMI) on the mean and extreme WP, SWH, and PWP that include variability due to ENSO is also provided in Supplementary Fig. 3.
Statistically significant IOD| ENSO influences on WPavg and Havg are limited in the Indo-Pacific Ocean and are generally less intense than ENSO influences (c.f. Figs. 2 and 3). During DJF and MAM, the positive responses of extreme WP and SWH to IOD| ENSO are evident over the SO, and the responses extend into the IO for PWP (Fig. 3). The high and low-pressure anomalies over the mid and high-latitude region of the Indo-Pacific Ocean produce strong winds and enhances the wave parameters (SWH and PWP) over the SO, resulting in enhanced WP over the SO during DJF and MAM (c.f. Figs. 1 and 3, and Supplementary Fig. 1). Significantly decreased signals are also found over the AS and central-to-western IO during MAM. However, the IOD is not active during this half of the year; therefore, such signals during independent IOD years (IOD| ENSO ) are related to the east-west gradient in SST anomalies over the equatorial Indian Ocean along with anomalous surface easterlies in Fig. 3 As in Fig. 2, but for theseasonalIOD influence independent of ENSO (denoted as IOD| ENSO ), obtained after the removal of ENSO signals spring (Chakravorty et al. 2013). Warming in the TIO leads to weakening wind motion and hence suppressed the wave climate as well as WP in the AS and central-to-western IO (Chakravorty et al. 2013;Yuan et al. 2008) (c.f. Figs. 1a and 3, and Supplementary Fig. 1). During JJA and SON, decreases in WP and SWH are evident over the majority of the eastern IO, with increases only in extremes in the BOB in JJA, and over the AS and southwestern IO in SON (Fig. 3a, b). During positive IOD (pIOD), BOB experiences high wave activities and hence WP, which presumably arises from enhanced wind during JJA Srinivas et al. 2021). The increased wave activities over BOB in JJA are indicated by positive responses in the SWH and negative in the Pavg (Fig. 3 and Supplementary Fig. 1). The opposite occurs for mean and extreme PWP, where weak decreases are found over the entire IO in JJA, but large increases are found over the eastern IO along side decreases over the western IO in SON. The IOD| ENSO influence on extreme WP and SWH is evident over the eastern PO in DJF, over the central north Pacific in MAM, over the WNP in JJA and SON (Fig. 3a, b). During positive IOD (pIOD) events, a similar spatial pattern as in WP over eastern PO in DJF and central north Pacific in MAM is observed in wind speed (c.f. Fig. 3 and Supplementary Fig. 1), which enforces similar variability in wind speeds and further in wave height and WP. The WNP is also subject to high WP due to intensified tropical cyclone activity during pIOD events in JJA and SON (Zhou et al. 2019); however, negative amplitudes in these regions suggest that El Niño hampers such activity and resulting in smaller WP(c.f. Fig. 3 and Supplementary Fig. 3). The mean responses to IOD| ENSO are also observed to follow similar patterns as the extreme, except for the western PO and BOB in JJA.
Overall, an increase in SWH and decrease in PWP over regions such as the BOB and the north-western Australian coast in DJF is associated with the seasonal increase in small fetch winds (Remya et al. 2020). In addition, the significant impact of the IOD| ENSO on SWH is constrained to the eastern IO and BOB in JJA, with decreases in mean PWP. This indicates that whilst swells dominate the IO, wind seas (directly generated and strongly coupled to local winds) are also of importance in JJA during positive IOD events (Srinivas et al. 2021;Remya et al. 2020). In SON, the strongest IOD| ENSO responses in PWP are evident over the entire IO, except the far western IO. However, in the PO, positive responses of PWP to IOD| ENSO occur over the eastern PO except in SON, where decreases in PWP occur over the majority of the PO (Fig. 3c).
Lastly, comparing independent IOD inf luences (IOD| ENSO ) to the original IOD signals (c.f. Fig. 3 and Supplementary Fig. 3), the independent IOD impacts on WP, SWH, and PWP are similar to the complete IOD signal, yet slightly reduced over the entire Indo-Pacific Ocean in DJF and MAM, and over the IO during SON. This emphasizes the significant influence of the IO climate variability over the Indo-Pacific Ocean in DJF and MAM, and over the IO in SON even in the absence of ENSO. In the PO, decreases in WPavg and Havg over the western NP in JJA and SON occur, indicating that ENSO plays a vital role in enhancing the IOD influences in this region (c.f. Fig. 3a, b and Supplementary Fig. 3a, b). Similarly, the negative responses of Pavg to IOD| ENSO are evident over the western NP in JJA and SON, yet they are positive when the covarying ENSO influence is included. This suggests that the PWP signals in the western NP are significantly subdued when the IOD and ENSO are in phase (c.f. Fig. 3c and Supplementary Fig. 3c).

PDO influence
Seasonal regression patterns of WPavg and WPmax, Havg and Hmax, and Pavg and Pmax against the ENSO| PDO (i.e., ENSO independent of the PDO variability) and PDO| ENSO (i.e., PDO independent of the covarying ENSO signals) over 1979-2019 in the Indo-Pacific Ocean are displayed in Figs. 4 and 5, respectively. In addition, the original ENSO and PDO influence on the mean and extreme WP, SWH, and PWP is also provided in Supplementary Fig. 2 and Fig. 4, respectively.
Overall, the ENSO| PDO influence on mean WP exhibits similar regional and seasonal variations as in the original ENSO but with a slight reduction in the amplitude throughout the year, apart from the PO in MAM, indicating the dominant impact of ENSO even in the absence of PDO (c.f. Fig. 4a and Supplementary Fig. 2a). In MAM, a decrease in WPavg is evident over the central Pacific. The mean wind speed (Wavg) response patterns to ENSO| PDO are largely consistent with the Havg and WPavg response patterns in the central Pacific, indicating that decreased mean WP is indeed induced by decreased wind speed energy (c.f. Fig. 4 and Supplementary Fig. 1). This reveals that PDO enhances the WP over the central Pacific in MAM (c.f. Fig. 4a and Supplementary Fig. 2a). The impact of the ENSO| PDO on WPmax is similar to WPavg yet with stronger amplitudes. The regression patterns of mean and extreme SWH associated with the ENSO| PDO are also consistent with the regression patterns of mean and extreme WP throughout the year (Fig. 4b). Further, the Pavg and Pmax response patterns to ENSO| PDO are similar to those of the original ENSO yearround except in MAM. In MAM, a reduction in response patterns of Pavg and Pmax to ENSO| PDO over the central NP (Fig. 4c) is associated with the warm ENSO phase.
For the independent PDO influence (i.e. PDO| ENSO ), significant increases in mean and extreme WP and SWH are mostly confined to the PO and most prominent in the NP (Fig. 5a, b). Over the IO, positive PDO| ENSO responses in WPavg and Havg are most prevalent during JJA. However, strong counter-responses (i.e. significant decreases in WPavg and Havg) are evident over the same regions during SON (Fig. 5a, b). In JJA, negative PDO (nPDO) strengthens the WPavg in the AS, due to an increase in the pressure gradient between the IO and the East Pacific (Figs. 1 and 5) (Odériz et al. 2021;Wang et al. 2008). In SON, enhancement  Fig. 2, but for the seasonal ENSO influence independent of PDO (denoted as ENSO| PDO ), obtained after the removal of PDO signals Influence of natural climate variability on extreme wave power over Indo-Pacific Ocean assessed… 1 3 Fig. 2, but for the seasonal PDO influence independent of ENSO (denoted as PDO| ENSO ), obtained after the removal of ENSO signals in WPavg in the BOB is associated with relatively more and intense (above-average) tropical cyclone activity during warm PDO phases (Girishkumar et al. 2015) (Fig. 5). Overall, the extreme responses to PDO| ENSO for WP and SWH are consistent with those of the mean responses. The strongest impact of independent PDO (i.e. PDO| ENSO ) on Pavg and Pmax is observed over the central NP in DJF and SON, and over the eastern and southern PO in MAM and JJA (Fig. 5c). The notable regions exhibit a substantial relationship, whereby changes in NP SST anomalies due to the warm PDO phase result in anomalously larger PWP. In DJF and MAM, PWP decreases and SWH/WP increases in the western NP are related to the seasonal increase in wind seas. In the IO, positive responses to PDO| ENSO in Pavg and Pmax are evident over the mid-latitudes of the SIO in DJF, and over the western IO in MAM. In JJA, an increase in Pavg and Pmax values occurs over the entire IO apart from a small part of the western SIO. Conversely, counter-responses in Pavg and Pmax (i.e. decreases over the IO) are found in SON.

Fig. 5 As in
Lastly, comparing the seasonal PDO influence independent of ENSO (i.e., PDO| ENSO ) to the original PDO signals (c.f. Fig. 5 and Supplementary Fig. 4), it is evident that excluding the co-occurring ENSO signals from PDO reduces the response amplitudes over the eastern PO and mid-latitudes of the SIO in DJF, western TIO, and SIO in MAM, WNP, and BOB in JJA, and WNP and SIO in SON. This reveals that ENSO plays a significant role in enhancing PDO influences in these regions during these seasons. However, enhanced WP also occurs over the WNP in MAM and the eastern Pacific in JJA (c.f. Fig. 5 and Supplementary Fig. 4).

Composite analysis of ENSO and IOD
Seasonal time series of mean WP (WPavg) and detrended ENSO, IOD, and PDO indices averaged over the Indo-Pacific Ocean (90° S-90° N, 20° E-70° W), PO (90° S-90° N, 120° E-70° W), and IO (90° S-30° N, 20° E-120° E) for the period 1979-2019 is presented in Supplementary Figs. 5-7. Further, the in-phase combinations of El Niño events with pIOD (brown color) and El Niño events with pPDO (orange color) are also highlighted (see Supplementary Fig. 5 and 6). Supplementary Fig. 5 highlights the in-phase combinations of El Niño events with pIOD coincide with the seasonal WP over the IO during JJA and SON whereas, the El Niño events with pPDO coincide with the seasonal WP over the PO year-round ( Supplementary Fig. 6). This suggests that in the Indo-Pacific Ocean, there is a strong interrelation between WP and prominent interannual climatic variability modes like ENSO, IOD, and PDO. To provide further insight into the interrelation between the various modes of natural climate variability, a composite analysis of the mean and extreme WP for different ENSO and IOD, and ENSO and PDO phase combinations is conducted for the 41 year period over the Indo-Pacific Ocean. In this section, composite analysis is conducted between ENSO and IOD. Simply, El Niño (ENSO +), La Niña (ENSO −), and positive and negative IOD (pIOD and nIOD, respectively) years are chosen from the detrended and normalized time series of the original indices when ENSO and IOD indices exceed a threshold value of ± 0.5 (list of years is provided in Table 3). This results in a total of 9, 3, 5, and 9 sample years in JJA and 11, 3, 4, and 12 sample years in SON for the combination of El Niño/pIOD, La Niña/pIOD, El Niño/nIOD, and La Niña/nIOD, respectively. The composite patterns of the mean (left panel) and extreme (right panel) WP anomalies in (a) JJA and (b) SON for various ENSO and IOD combinations are shown in Fig. 6.
The WPavg and WPmax increase during the El Niño/ pIOD years and decrease during La Niña/nIOD years over the western PO, BOB, western TIO, and western SIO in JJA and the western PO in SON (Fig. 6a, b). In the BOB, El Niño enhances WP during JJA, which presumably arises from enhanced winds during JJA, and further intensified when ENSO and IOD co-occur in a positive phase combination. These results are in line with previous studies that analyzed the impact of the ENSO and IOD   1982, 1983, 1991, 1993, 19941999, 2007, 2008DMI(−) or nIOD 1990, 1992, 2002, 20041981, 1984, 1989, 1995, 1996, 1998(b) SON DMI( +) or pIOD 1982, 1986, 1987, 1991, 1994, 20021983, 1985DMI(−) or nIOD 1979, 20031981, 1984, 1988, 1989, 1995, 1996, 1998, 1999 on wave parameters (Sing et al. 2001;Kumar et al. 2019;Srinivas et al. 2021) (Figs. 2, 3, and 6a). Conversely, La Niña or nIOD events amplify tropical cyclonic activities and hence WP over the BOB during SON, more so when La Niña co-occurs with a nIOD (Girishkumar and Ravichandran 2012;Kumar et al. 2019;Mahala et al. 2015;Srinivas et al. 2021) (Figs. 2, 3, and 6b). The combination of an El Niño event with a pIOD (or nIOD) leads to an increase in mean and extreme WP over the western NP and counter-response is evident for the combination of La Niña with pIOD (or nIOD) in JJA and SON, which reveals the strengthening of ENSO in enhancing/reducing WP in western NP (Fig. 6a, b). During out-phase combinations (i.e.El Niño/nIOD and La Niña/pIOD),an increase in mean and extreme WP is observed over the south-east Indo-Pacific Ocean during La Niña/pIOD and decrease during El Niño/nIOD in JJA and SON.

Composite analysis of ENSO and PDO
The  Table 4). This yields a total of 8, 5, 2, and 8 sample years in DJF, 13, 5, 3, and 11 sample years in MAM, 7, 3, 6, and 8 sample years in JJA, and 12, 5, 2, and 12 sample years in SON for the combination of El Niño/pPDO, La Niña/pPDO, El Niño/nPDO, and La Niña/nPDO, respectively.  Table 3) For El Niño/pPDO events, WPavg increases over the eastern PO in DJF, the central NP in MAM, NPO, SIO, BOB, and western TIO in JJA, and western PO in SON (Fig. 7, left panel). Decreases in WP during this phase combination occur over the NIO, TIO, SCP seas, and WNP in DJF, WNP, and eastern South Pacific (SP) in MAM, eastern SP in JJA, and in the eastern PO, NIO, and TIO in SON. Similar yet oppositely signed patterns are observed during La Niña/nPDO (Fig. 7, left panel). Apart from coastal regions of the western NP, an El Niño (La Niña) event with a pPDO leads to a significant increase (decrease) in WPavg in DJF (Fig. 7a, left panel). As, El Niño events amplify the extra-tropical wave climate in the NP as the ENSO warm phase is connected with a strengthened Aleutian Low (Li et al. 2015). This effect is further intensified when ENSO and PDO are in a positive phase combination (Bonsal et al. 2001;Kumar et al. 2016), resulting in enhance wave climate and WPavg over PO (Fig. 7a). The increase in WPavg is seen over the larger parts of the NIO and TIO in MAM during in-phase combinations (i.e., El Niño/pPDO or La Niña/nPDO) (Fig. 7b, left panel). In WNP, WPavg increases for the combination of El Niño with a pPDO (or nPDO) and decreases for the combination of La Niña with a pPDO (or nPDO) in JJA and SON. This indicates that the ENSO plays a substantial role in enhancing (and also subsiding) the WP over the western NP in JJA and SON, in agreement with other studies Oh 2020, 2018) (Fig. 7c, d, left panel). Further, a La Niña event associated with a pPDO, enhances the WPavg over the IO, whereas counter-responses are evident for the combination of a La Niña with nPDO in JJA. The combination of an El Niño (or a La Niña) with pPDO, decreases the mean WP over large parts of the IO, while increases for the combination of an El Niño (or a La Niña) with nPDO in SON. When ENSO and PDO occur out of phase (i.e. El Niño/nPDO and La Niña/pPDO), resultant patterns are noisy and even change the sign in DJF, depicting a decrease in WP over the larger parts of the Indo-Pacific Ocean in MAM, and an increase in WPavg over the BOB and western TIO and decrease in WPavg over the eastern PO in JJA. In SON, an enhancement in WPavg is observed over the larger parts of the IO, western PO and mid-latitudes of the SP during El Niño/nPDO events and decreases during La Niña/pPDO (Fig. 7d). The impact of the ENSO and PDO combinations on extreme WP extreme appears over the same region as in the mean WP year around (Fig. 7, right panel).

Summary and conclusions
This study investigates the impact of natural climate variability modes such as ENSO, IOD, and PDO on seasonal extreme WP in the Indo-Pacific Ocean using ERA5 reanalysis data over the period 1979-2019. A non-stationary GEV distribution is applied on the seasonal extremes to determine the regions with significant impact, where the natural climate variability modes are taken as the covariates. In addition, the response patterns of SWH, PWP, wind speed, SST, and SLP to climate variability modes are also evaluated to understand the underlying physical mechanism involved for inducing variations (i.e. increasing or decreasing) in the WP extremes.
Overall, each climate variability mode exhibits distinct seasonal impacts on the extreme WP in the Indo-Pacific Ocean, which is driven by corresponding changes in atmospheric circulation and wind speeds. The strongest positive ENSO| IOD influence on extreme WP is evident in DJF over the northeast NP, ITCZ, and SPCZ regions, whereas the WNP and MC exhibit counter-responses. The changes in WPmax during DJF are associated with anomalous wind speeds driven by an anomalous high-low pressure system. Seasonal variability of ENSO| IOD responses enhances the WPmax over the WNP during JJA and SON, and BOB during JJA, as El Niño amplifies the tropical cyclone activities over these regions. El Niño suppresses the WPmax over the TIO in DJF by weakening the Walker cell and trade winds, and La Niña enhances the WPmax over the AS in JJA by inducing strong pressure gradient between the IO and East Pacific. The positive responses of extreme WP and wind speed to IOD| ENSO are observed over the eastern Pacific and SO in DJF and the central north Pacific and SO in MAM. Warming in the TIO weakens the wind motion and hence suppresses the wave climate as well as WP in the AS and central-to-western IO in MAM, whereas pIOD events enhance the WPmax over the BOB in JJA, which presumably arises from enhanced winds in the BOB. Decreased signals in WPmax to ENSO| IOD over the WNP during JJA and SON suggest that El Niño hampers such activity, resulting in smaller WPmax. The ENSO| PDO influence on extreme WP exhibits similar regional and seasonal variations as in the original ENSO but with a slight reduction in the amplitude throughout the year apart from the Pacific in MAM. For the PDO| ENSO influence, significant increases in extreme WP are mostly confined to the Pacific and most prominent in the NP. Over the IO, positive PDO| ENSO responses in WP are most prevalent during JJA and over the SIO and eastern IO. Due to an increase in the pressure gradient between the IO and the East Pacific, negative PDO intensifies WP in the AS during JJA, whereas positive PDO reinforces tropical cyclone activities in the BOB during SON and enhances WP.  Table 4) ◂ The independent seasonal influence of each climate mode on mean and extreme WP, SWH, and PWP was compared with the original to assess the role of one variability mode in strengthening or weakening the influence of another variability mode. The ENSO influence on extreme WP, independent of IOD, exhibits enhanced WPmax over the eastern TIO in JJA and over the eastern TIO and central NP in SON compared to the original ENSO signals. This implies that the IOD reduces the ENSO signals in these regions during that time of year. The independent IOD impact on WP shows a decrease in WPmax over the western NP in JJA and more so in SON. This suggests that ENSO plays an important role in enhancing the IOD influence in this region during JJA and SON. The independent ENSO influence on WPmax, obtained after the removal of PDO, reveals that the PDO has little to no influence over ENSO signals in the Indo-Pacific Ocean except in MAM. In MAM, the PDO has a strong impact on the influence of ENSO in the PO. Lastly, the independent PDO impact, after removing the ENSO signals, is related to a decrease in WPmax over the eastern PO in DJF, and western NP in JJA and SON. This demonstrates that ENSO is responsible for increasing the WP in these regions during that time of the year. In MAM, ENSO reduces the PDO signals over the PO. In addition, seasonal SLP teleconnection patterns regressed against ENSO| IOD , IOD| ENSO , ENSO| IOD , and PDO| ENSO , exhibit a high and low-pressure anomaly that in turn generates strong winds (Kumar et al 2016Patra et al. 2020;Remya et al. 2020;Yang and Oh 2018) and consequently enhances the wave parameters (i.e. Hs and Tp) in the respective localized regions. Overall, the mean WP patterns were highly correlated with the extreme WP patterns year-round. Maximum WP increases were often found during seasons when there are increases in tropical cyclone activity and strong winds, such as NIO during JJA.
Composite analysis of mean and extreme WP for the different phase combinations of natural climate variabilities (i.e. ENSO with IOD and ENSO with PDO) strengthen the conclusions drawn from the independent influence patterns (i.e. ENSO, IOD, and PDO separately), which shows that the IOD (or PDO) plays an important role in enhancing or reducing the intensity of ENSO-related responses, or vice versa, depending on the season. During JJA, the IOD enhances (reduces) the ENSO impact on WP when both are in-phase (out-phase) combinations. In SON, (i.e., when ENSOs generally develop and IODs reach in its mature phase), ENSO is able to enhance the IOD influence on WPavg and WPmax significantly. While, PDO (i.e. pPDO or nPDO events) enhances (reduces) the ENSO influence on WP during El Niño (La Niña) year-round.