Offshore wave climate of the Great Barrier Reef

The Great Barrier Reef (GBR) is the largest coral reef system on earth, with ecological and scientific importance for the world and economic and iconic value for Australia. However, the characterisation of its offshore wave climate remains challenging because of its remoteness and large dimensions. Here, we present a detailed analysis of the offshore wave climate of the GBR, unveiling the details of both modal conditions and extreme events. We used a calibrated satellite radar altimeter dataset (spanning from 1985 to 2018) to quantify wave climate, assess the influence of climate drivers, and analyse the wave conditions generated by tropical cyclones at three main regions of the GBR (northern, central, and southern). Our results indicate average significant wave heights of 1.6 m, 1.5 m, and 1.7 m for the northern, central, and southern GBR, respectively. The modal wave climate exhibits substantial seasonality, particularly in the northern region with dry season wave heights up to twofold larger than during wet season. The northern and central wave climates show decreasing wave height and wave energy trends over the last 33 yrs, whilst the southern region remains stable. Consistent with prior studies, we found that the wave climate in the southern region is modulated by the El Niño-Southern Oscillation and the southern annular mode, with influence additionally extending to the central region. Analysis of the extreme waves generated by tropical cyclones revealed they generate large, long period waves, frequently above 7 m, resulting in wave power up to 32-fold higher than median conditions.


Introduction
Ocean waves are a fundamental driver of reef and coastal ecosystem processes. For coral reefs, waves are both constructive and destructive forces, being instrumental for growth and development of coral environments (Dollar 1982); they can also cause coral death and subsequent sediment rubble production (Etienne and Terry 2012). Likewise, coral reefs interact with waves and significantly decrease the amount of energy transported across the reef through bottom friction and dissipation (Harris and Vila-Concejo 2013). The largest coral reef system in the world, the Great Barrier Reef (GBR), is located offshore North-East Australia in the Coral Sea. Stretching over 2700 km, it is one of the most biodiverse ecosystems and an important refuge for both endemic and migratory species (Hopley et al. 2007). It plays a pivotal role in protecting the Queensland coast from offshore extreme waves, as it is highly effective at reducing wave energy. The offshore reef matrix significantly attenuates wave height through wave shadow effects, bottom depth, and friction (Young 1989;Young and Hardy 1993;Gallop et al. 2014); waves in the lee of the reef are predominantly locally generated wind sea wave (Gallop et al. 2014). Tropical cyclone (TC) waves have also been shown to attenuate over the GBR (Young and Hardy 1993), reducing nearshore wave height and runup height by 1.5-2 times the offshore wave height (Callaghan et al. 2020). Several wave buoys along the Queensland coast provide measurements of inshore, locally generated, wind waves produced in the lee of the reef. However, mostly due to its large spatial extent and its isolation that both preclude long-term offshore monitoring deployment, the seaward wave climate directly influencing the GBR has never been fully characterised (Hopley et al. 2007).
Wave climate of the region was surmised by Hopley (1982) to 1.15 m median significant wave height (H s ), exceeding 3.99 m only 0.01% of the time, with maximum significant wave height ( H max s ) of 8.5 m. These estimates were based on the wave conditions measured during a 1970 beach erosion study at the Gold Coast, over 500 km south of the GBR (Delft Hydraulics Laboratory 1970). Several other studies have investigated wave conditions based on numerical wave modelling and remote sensing techniques. Gallop et al. (2014) analysed the modulation of waves through the GBR matrix, finding that 95% of waves to the east of the GBR were attenuated and that waves in the GBR lagoon were predominantly wind-generated waves. As a result, the series of wave buoys along the inshore Queensland coast only provide partial wave climate information and do not represent the offshore conditions seaward of the reef matrix. Hemer et al. (2011) conducted an ocean-basin scale study of the Pacific Ocean wind wave climate using a combination of altimeter observations, hindcast models, and buoy records. Their analysis determined that south-east trade winds and cyclones are the dominant offshore wave generators for the region, modulating both the modal and extreme wave climates. Additionally, Young and Donelan (2018) performed a global study on wave heights and determined that the Coral Sea had a mean H s between 1.5 and 2.5 m, depending on the season and latitude. Gallop et al. (2014), using a combination of wave hindcast data and altimeter data, found that H s varied little, between 1.6 and 1.8 m, along the 2000 m depth contour offshore the GBR. However, at the 100 m depth contour closer to the reefs, H s varied significantly, where the northern region (12° to 14° S) had a mean H s of 1.7 m, decreasing to 1.5/1.6 m in the central region (15° to 21° S) and increasing to 1.75 m south of 21° S. From their study, wave direction was predominantly from the south-east, changing to a more easterly direction as latitude increased.
Climate drivers have also been shown to influence wave climate within the Australian East Coast region. The El Niño-Southern Oscillation (ENSO) phenomenon is the largest and most influential mode of climate variation that operates on a seasonal-to-interannual timescale (Stopa andCheung 2014, Timmermann et al. 2018). The positive La Niña phase leads to reduced atmospheric convection over the Pacific Ocean, causing a greater number of TCs (Jin et al. 2014) and stronger than normal trade winds, both of which could lead to larger wave heights (Hemer et al. 2011). In contrast, the negative El Niño phase leads to a shift in atmospheric circulation, with a weakening or reversal of the dominant south-easterly trade winds and decreased frequency of TC for Australia (Timmermann et al. 2018). At Fraser Island just south of the GBR, La Niña is significantly correlated with larger wave heights (mean H s of 2.01 m) propagating from a more easterly direction and more frequent storm events than during El Niño phases (mean H s of 1.88 m) (McSweeney and Shulmeister 2018).
The southern annular mode (SAM) also has a significant impact on the Coral Sea H s above 23.5°S (Hemer et al. 2011, Marshall et al. 2018. The SAM is a climate driver that influences the north-south movement of strong westerly winds, thereby influencing rainfall, temperature, and waves across Eastern Australia. The timing of positive, neutral, and negative phases of the SAM is random and can last for 1 to 2 weeks. Easterly and westerly wind anomalies during the positive and negative phases, respectively, impact the mean wave height and the occurrence of daily low and high wave conditions (5th and 95th percentile) (Marshall et al. 2018).
The extreme wave climate in the region is predominantly controlled by TCs that can severely damage marine biota, in addition to human life and infrastructure (Beeden et al. 2015;Vila-Concejo and Kench 2017). Despite the important role of TCs in reef and rubble development, recovery can be compromised by multiple stressors endangering the resilience of reef ecosystems and have wider ecological effects. For example, Gerlach et al. (2021) assessed the longterm impacts of TCs on coral cover and fish populations and connectivity at the Capricorn-Bunker group of reefs in the southern GBR. They found that coral cover largely disappeared after TC Hamish (March 2009, Category 5) tracked directly along the reef matrix, with a reduction in total hard coral ranging from 51 to 98%. Partial recovery of between 50 and 60% occurred within 6-8 yrs indicating a gradual recovery after TC devastation. The resultant significant habitat change following a TC also leads to changes in fish species richness, genetic diversity and population levels (Gerlach et al. 2021).
However, despite TCs generating powerful waves with potentially devastating impacts for coral reefs, knowledge of the wave conditions generated during these events is still a developing field of research, particularly for offshore the GBR. TCs are defined by wind strength, and thus, the wave conditions generated for each category are often not known; wave conditions depend on wind intensity, duration, direction and speed of the TC, as well as the characteristics of the fetch and local bathymetry. A global study of extreme wave heights using satellite altimeter data (Vinoth and Young 2011) indicated a 100-yrs Average Return Interval (ARI) of wave heights of 8-10 m within the Coral Sea region, likely related to an extreme TC. A more recent detailed analysis of synthetic TCs that tracked within the GBR corroborates the 8 m 100-yrs ARI wave height along the length of the GBR, with reduced exposure at the northern reefs (Callaghan et al. 2020). The 1% maximum H s ranges from 1 to 10.5 m, depending on reef exposure and available protection from existing reef matrix (Callaghan et al. 2020).
Here, we use satellite altimetry data to analyse waves offshore the GBR with a threefold objective: (1) we establish the modal offshore wave climate of the GBR; (2) we evaluate the effects of large-scale climatic forcing (e.g. ENSO and SAM) on the regional wave climate; and (3) we determine the impact of TCs on the offshore wave climate.
Whilst these aims have been addressed before, we build on existing knowledge and provide greater spatial and temporal detail of the wave climate directly impacting the Great Barrier Reef, contributing detailed statistics of wave climate and the driving forces to the current knowledge base. The impacts of tropical cyclones on wave conditions have similarly been assessed over multiple decades; we provide the first analysis of altimeter-observed waves directly related to cyclones within the GBR region.

Methods
Satellite radar altimeters have been widely established as a pinnacle remote sensing technique to determine wave climates globally, with high spatial-temporal density (Vinoth and Young 2011;Zacharioudaki et al. 2015;Godoi et al. 2016;Ribal and Young 2019). Altimeters interpret a reflection of the sea surface across a footprint of 7-10 km wide, determining the H s and wind speed (U 10 ) over this footprint, instead of individual waves. This technique has been applied in numerous wave climate studies and is particularly suited for remote locations such as the Coral Sea (Gallop et al. 2014;Young and Donelan 2018). This is due to the low-cost, wide geophysical observation regions available, limited availability of long-term wave buoy recordings, and difficulty accessing remote areas to set-up and maintain buoys and other wave-measuring equipment. A 33-yrs record  of thirteen satellite radar altimeters was obtained from the Australian Ocean Data Network, where altimeter observations have been extensively calibrated to buoys, cross-validated to other altimeters, and quality controlled to remove data errors and spikes . Accuracy assessment of altimeter-derived wave heights against wave buoys data shows that 95% of these data were within ± 0.5 m for offshore data (RMSE of only 0.19 m from a 9-yrs of wave analysis in the Gulf of Cadiz) (López-García et al. 2019). This accuracy might change between satellites as shown in Ribal & Young (2019)- Table 4. H s and U 10 were used to calculate wave period (T z ) and wave energy (P) in order to characterise wave climate of four different locations offshore the GBR (Fig. 1) and to quantify the conditions generated by TCs.

Wave climate statistics
We developed a Python package, RADWave , to analyse altimeter observations with a data quality flag of "good" . RADWave uses U 10 and H s to determine T z and P for each altimeter observation. To determine T z , a genetic algorithm created by Govindan et al. (2011) was used (Eq. 1), which has a root mean square error of 0.76 s: where ɛ refers to wave age (Eq. 2), calculated as: with g the acceleration by gravity (9.8 m/s 2 ). Linear wave theory was used to calculate P, which incorporates both H s and T z . In deep water, P can be determined through the following equations (Airy 1841). First, mean wave energy density (E) is calculated by: where ρ is the density of seawater (1027 kg/m 3 ) using a mean salinity value of 35.49 ppt from Heron Island, south GBR averaged over 2009-2019, and mean temperature of 24.3 °C (Fabricius et al. 2020). Wave group velocity (C g ) in deep water is then calculated by Eq. 4, using T z as determined in Eq. 1: Wave power P can therefore be calculated through which is the wave energy flux per metre of wave crest (W/m). This is converted to kW/m for ease of analysis.

Study areas
The standard approach for wave climate analysis from altimeters consists of defining an area and combining the (1) available altimeter datasets over a long period, to overcome the inherent limitation of high spatial yet low temporal data density of this type of data (Vinoth and Young 2011;Young and Donelan 2018). A key underlying assumption in the method is that it assumes homogeneous waves within the region of interest for any specific time; however, the validity of this assumption decreases as the spatial extent of the region increases. Here, we selected four 1 × 1° regions (R1-R4) offshore the GBR in the Coral Sea ( Fig. 1), in line with recommendations from Vinoth and Young (2011); regions are approximately 111 km × 111 km in size. The four regions were selected to incorporate a range of latitudes, be adjacent to reefs and be located > 50 km from reef or land to eliminate their interference in altimeter signals. The regions are referred to as north (R1), central (R2 and R3), and south (R4), with the extents of each region indicated by the bounding boxes in Fig. 1.
The modal wave climate was analysed using RADWave for each of the four identified regions over a 33 yrs period, using the median value of each satellite pass to ensure independence of observations, following Vinoth and Young (2011). The overall median, mean, 95th percentile, and maximum values were calculated per region for each parameter (H s , T z and P). To determine monthly and seasonal changes, the mean and 95th percentile value for each month was then calculated between 1993 and 2018, providing a consecutive regional monthly dataset (Hemer et al. 2007;Godoi et al. 2016;McSweeney and Shulmeister 2018). Storm conditions Fig. 1 Four Coral Sea study regions; R1 is the northern region, R2 and R3 are the two central regions, and R4 is the southern region were defined as the H s 95 over the whole Coral Sea study region, where all altimeter records within the Coral Sea, not just the four study regions, were analysed to obtain H s 95 . To determine storm conditions for each study site, a storm is defined as when the median value of all satellite tracks over a particular day is greater than the long term H s 95 of the whole Coral Sea (here defined as 143-155° E, 10-24° S), to enable each region to be compared against a consistent value (Masselink et al. 2014, e.g. Castelle et al. 2015.

Seasonal changes and decadal trends
Seasonal trend analysis was performed by comparing monthly mean and 95th percentile values for each identified region (R1-R4), allowing the analysis of wave climates on both a monthly and seasonal scale. This approach was also used to compare changes between the austral wet (November-March) and dry (April-October) seasons, the two distinct seasons in Northern Australia close to the tropics.
Statistically significant decadal monotonic trends were determined by performing a Seasonal Mann-Kendall test for both mean and 95th percentile values of each parameter and for each region (R1-R4). This test was run on each season (here defined as wet or dry, n = 2) and then summed to provide an overall statistic determining trend between 1993 and 2018. The technique is a nonparametric method and can handle missing data; it is less influenced by outliers and has been similarly applied in wave climate studies Stopa et al. 2016;Godoi et al. 2018).
The influence of climate oscillations on wave climate was assessed by comparing the variance of the monthly mean values of each oscillation to the monthly mean values of the wave climate parameters for each region. ENSO phases were calculated from the Southern Oscillation Index (SOI), where positive SOI values indicate La Niña and negative indicate El Niño. Monthly SOI data were sourced from the National Oceanic and Atmospheric Administration (2019). SAM phases were determined using the Southern Annular Mode Index (SAMI) and were calculated from monthly values (British Antartic Survey 2019). For both indices, the mean value over the study period 1993-2018 was calculated. The overall mean value is then subtracted from the monthly means, thus calculating monthly anomalies and variation from the mean value (Godoi et al. 2018). Determination of anomalies was also performed for monthly mean and 95th percentile of H s , T z and P extracted from the altimeter dataset between 1993 and 2018. Finally, statistical correlations between climate oscillation and mean and extreme wave parameter anomalies are represented by calculating the Pearson's correlation coefficient at 95% confidence.

Tropical cyclones
Extreme wave analysis was performed using RADWave ) to identify and extract altimeter observations that occurred close to TC tracks, as TCs are the primary generators of extreme waves in the Coral Sea. RAD-Wave allows the identification of existing altimeter data observations closest to the cyclone eye within 6 h of the cyclone passage and extract altimeter information from each identified position close to any specified TC.
We analysed 53 TCs over 29 cyclone seasons that passed through the Coral Sea region, here defined as 143-155°E, 10-24°S. The 29 cyclone seasons were: 1985-86, 1986-87, 1987-88, and from the 1992-93 season to the 2017-18 season. Six-hourly track records were sourced from a cyclone track database (Bureau of Meteorology Australia 2019a). Each cyclone was sorted into Categories 1 to 5 based on maximum mean wind speed reached within the Coral Sea study region (with Category 5 as the most intense based on the Saffir-Simpson scale), and the maximum observed value of H s , T z and P was calculated for each cyclone, denoted as H max , T zmax , and P max . For each Category, the mean from all applicable cyclones was determined for each parameter, in addition to the maximum recorded for the considered category. An in-depth analysis was performed for Severe Tropical Cyclone Justin (Bureau of Meteorology Australia 2019b), a Category 3 cyclone that generated the largest wave observations of all investigated cyclones.

Results
This section presents our results for the Coral Sea wave climate, including seasonal changes, decadal trends and climate oscillations, and TC-generated waves.

Wave climate statistics
The modal wave climate is significantly different for each region, with clear latitudinal changes (Table 1). The northern region (R1) has high overall median, mean and 95th percentile wave conditions of both H s and P, with a mean H s of 1.6 m, and mean P of 36 kW/m. Waves decrease in size and energy in the central two regions, particularly R2, which has a mean H s of 1.4 m and mean P of 26 kW/m. R3 has a mean H s of 1.5 m and mean P of 31 kW/m. H s and P subsequently increase at the southern region (R4) to a mean H s of 1.7 m and mean P of 42.2 kW/m. H max does not follow this spatial distribution, as a single large storm can result in a significant outlier. Despite having the lowest mean H s , the central region at R3 records the highest H max of 6.8 m, generated by Severe TC Justin that tracked within 230 km of R3 in 1997.
T z follows a similar spatial distribution to H s and P, with longer period waves in the northern (R1) and southern (R4) regions and shorter periods in the central regions (R2 and R3); however, T z does not vary meaningfully between regions, especially when considering the accuracy of the T z calculation (RMSE = 0.76 s). All regions exhibit mean T z between 5 and 6 s, indicative of locally generated wind sea.
We calculated the storm threshold over the Coral Sea to be 2.9 m (H s 95 of the whole Coral Sea) ( Table 1). The northern and southern regions had the highest number of storms over the 33-yrs period with 166 events for R1 and 173 for R4, significantly higher than the two central regions (61 and 71 storms for R2 and R3). The impact of storms on wave height, alongside seasonal patterns and overall trends, is plotted in Fig. 2

Seasonal changes
Seasonal changes to wave climate are particularly evident in the northern region (R1) between wet season and dry season months, with H s and P doubling in the dry season compared to wet season (Fig. 3). The central and southern regions (R2-R4) do not show any clear wet-dry season changes. For these three sites, the trend changes from a high H s during March-April and decreases to a minimum H s at the beginning of the wet season in September. These trends similarly occur with P (Fig. A1). In contrast, T z does not follow significant seasonal trends across the Coral Sea region, with the largest change between monthly mean values of 0.4 s occurring in the northern region (R1) (Fig. A2).

Decadal trends
Overall mean value trends for each parameter during the period 1993-2018 are shown in Table 2. The northern and central regions (R1 to R3) exhibit a significant negative trend in H s and T z ; the southern region (R4) shows no trends. The northern region (R1) shows a decrease in H s of approximately − 0.3 cm/yr, whilst the two central regions (R2 and R3) decrease in H s at approximately − 1 cm/yr (Table 2). T z is decreasing at a rate of − 0.01 s/yr at all three northern regions (R1-R3). In the central regions (R2 and R3), P is decreasing at − 0.39 and − 0.29 kW/yr, respectively. Interestingly, the decreasing trend in H s height in the northern region (R1) is not sufficient to elicit a trend in P (Table 2). No decadal trends were observed for the extreme (95th percentile) value for each parameter in the studied regions; therefore, whilst mean values are decreasing at the northern and two central regions (R1-R3), extreme values remain constant across the Coral Sea.

Climate oscillations
Climate oscillations have a significant influence on mean and extreme monthly wave climate anomalies, particularly in the two central and the southern regions (R2-R4) ( Table 3). A positive correlation between the SOI and mean monthly anomalies exists in regions R2-R4, indicating increased wave heights occur during La Niña phases (p < 0.05) ( Table 3). Modulation of wave climate is strongest at the southern region (R4), with SOI positively correlated with all parameters for both mean and extreme (95th percentile) monthly anomalies. For example, 47.5% of monthly mean H s anomalies are explained by ENSO for R4 (Table 3). Correlation with mean and extreme H s and P is also present up to the central regions at R2 and R3; however, T z is not influenced, suggesting that ENSO predominantly influences wave height, particularly towards the northern limit. The northern region (R1) monthly anomalies are not significantly correlated with ENSO, except for T z 95 (Table 3).
SAM also modulates the wave climate of the Coral Sea with a similar spatial pattern to ENSO occurring along a latitudinal gradient (Table 3). SAM significantly influences the southern region (R4) mean monthly values, for example, accounting for 20.5% of H s monthly anomalies, and 10% of T z and P. At R3 in the central region, all mean monthly parameters are significantly correlated with SAM, accounting for 10-20% of anomalies. H s and P continue to be modulated north to R2, where both monthly and extreme values are positively correlated. In the northern region (R1), no parameter, with the exception of T z 95 , is modulated by SAM, similar to ENSO (Table 3). Thus, spatial differences in strength of modulation are apparent, with high modulation by both indices in the south, decreasing in importance at the central region, to limited influence in the northern region.

Tropical Cyclones
Analysis of the TCs that tracked through the Coral Sea over the study period reveals that they predominantly occur from January to March, where March was the highest frequency month with 17 cyclones (Fig. 4). The most frequent cyclone category was Category 1, with a total of 15 TCs. Most years had at least one cyclone track through the Coral Sea, with a maximum of five cyclones occurring over the 2005-2006 season. Table 4 presents the mean maximum wave parameters calculated for each TC category and the highest maximum altimeter observation for each category. The values for wave parameters generally increase with cyclone intensity, with Category 5 having the highest mean maximum values for H s and P (5.9 m and 620 kW, Table 4). The mean maximum H s for all categories is larger than the Coral Sea storm threshold of 2.9 m, indicating that cyclones are higher intensity than common storms. T z has similar mean maximum values of 8 s for all categories. The influence of TCs on waves is demonstrated through analysis of individual satellite observations from each track. As an example, Fig. 5 presents the altimeter observations during severe TC Justin. Waves larger than the storm threshold of H s 95 (2.9 m) were observed across the Coral Sea, demonstrating that cyclones have significant impacts over a large area, and not just close to the cyclone eye. However, as altimeter observations can significantly undersample or entirely miss cyclone events, there are inherent limitations of applying these observations to determine accurate trends and perform detailed analysis for short-term events, in contrast to using altimeters for long-term analyses. In the absence of many direct observations in the Coral Sea, this initial dataset provides a first-pass assessment of cyclone conditions that directly impact the Great Barrier Reef on a broad scale, and not on an event-by-event basis. The extra scrutiny and judgement required when assessing the usefulness of altimeter data is apparent when comparing the highest maximum H s across all categories; the Category 3  result is higher than the Category 5 result. It is expected that the Category 5 highest maximum H s would be higher than Category 3, highlighting the extra caution required when interpreting and extrapolating altimeter observations and analyses in this context of event-based assessments. The highest observed wave conditions over the 33-yrs study period were generated by Severe Tropical Cyclone Justin, which lasted for 19 days. Reaching only Category 3, the cyclone produced maximum observed wave conditions of 9.58 m H s , 12.96 s T z and 2335 kW P, recorded 270 km from the cyclone eye (Fig. 5). The H s was more than 300% higher than the mean maximum conditions for Category 3 cyclones (calculated to be inclusive of TC Justin), and P was 117 times larger than the median P for the closest study region (R3, central region, Table 1). The effects of TC Justin were observed at significant distances from the cyclone; for example, 4.4 m waves were recorded 630 km away from the cyclone track. Figure 5 provides an extract of satellite altimeter observations within 3° (approx. 330 km) of the cyclone eye and within 3 h either side of the cyclone track. This demonstrates that large waves can travel in all directions from the cyclone eye for substantial distances; coral reefs not directly near a cyclone track can be affected. Despite only being a Category 3 cyclone, TC Justin produced the largest waves of all cyclones observed, possibly related to its lengthy duration and slow movement.

The wave climate of the Great Barrier Reef
Our analysis of 33 yrs of altimeter observations of the Coral Sea shows that the modal wave climate is spatially distinct across the Coral Sea with conditions changing along a latitudinal gradient. This is in accordance with Hemer et al. (2017), who used a WaveWatch III wave hindcast model validated against wave buoys and satellite altimeter data to determine Australian wave energy resources and found that the southern regions of the Coral Sea had mean wave heights of ~ 1.5 m, similar to that determined in this study of 1.7 m (R4). Hemer et al. (2017) proposed that the wave climate of the Australian Eastern Coast should be divided at the Tropic of Capricorn (23° S), which aligns with R4 in the present study, with areas to the north experiencing a smaller H s compared to larger in the southern regions (Table 1). The present study builds upon the findings of Hemer et al. (2017) to provide a specific reference with detailed analysis of wave climate impacting the GBR, with results and discussion focussing on the regional scale, in comparison with an Australian or global scale. The results are also similar to that of Young and Donelan (2018), whose study using a similar altimeter dataset indicates a smaller mean wave climate in the central areas of the GBR and increased wave heights at the northern and southern extents.
Our results suggest that the GBR has three distinct offshore wave climates: northern, central, and southern. These are characterised by differing modal and extreme wave parameters and storm exposure, trends, and modulation by large-scale climatic oscillations. The distinctions between the three proposed wave climates are presented in Fig. 6, depicting the location of our four regions (R1-4), latitudinal change in parameters, direction of trend, and the spatial extent and relative importance of each forcing mechanism.
The northern wave climate is characterised by higher waves than the central region, and by substantial variation in wave height between seasons; dry season H s and P mean values are twice as high as the wet season mean values. We posit this is related to changes in the strength of the southeast trade winds during the dry season. Additionally, the reef orientation and limited number of reefs in this area enables high exposure to waves from the north, east, and south-east and uninterrupted fetch for the trade winds to produce wind waves.
The central wave climate (R2 and R3) is characterised by lower mean H s and P through all seasons in comparison with both the northern (R1) and southern (R4) wave climates (Table 1). There is a reduced seasonal pattern with less differences between months or wet and dry seasons (Figs. 3 and  A1). Additionally, we have identified that the central region experiences the highest number of H s outliers of all studied sites (Fig. 3); R3 had the most wave P outliers and R2 equal second highest number of outliers, as shown in the P mean monthly graphs (Fig. A1). This means that the central region experiences more extreme events that generate conditions far larger and more powerful than modal conditions. For example, TC Justin tracked through the central region, generating waves > 9 m H s and P more than 40 times higher than modal conditions (Fig. 5).
The southern region has H s , T z , and P values slightly higher than that experienced in the northern region (Fig. 6b) and substantially larger than the central region. Additionally, seasonality trends in the southern region are slightly more pronounced than in the central wave climate region. The region is highly exposed to waves from the north, particularly the north-east, a key TC generation area. It is also exposed to waves from the east and south-east, meaning that waves from extra-tropical storms can propagate into the region with limited dissipation or loss of energy.

Decadal trends and climate oscillations
The northern region experienced a slightly decreasing trend in H s , whilst analysis of modulation by ENSO and SAM reveals that neither index significantly influences the wave climate in the northern region. To explain the seasonality experienced, we propose that the location of the Intertropical Convergence Zone (ITCZ), its strength, and associated weather patterns including the Australian Monsoon influence the northern wave climate. During the dry season, the ITCZ moves north, away from Australia (Vincent et al. 2011), leading to stronger south-east trade winds and subsequently Fig. 6 Wave climate variations along a latitudinal gradient in the Coral Sea, depicting changes between the three wave climate regions. a Queensland coastline with regions 1-4. b Changes in mean H s , T z and P, respectively, as latitude increases, where dots indicate study sites. c Direction of decadal trends of H s , T z indicating a negative trend for the northern and central regions, and no trend for the southern region, and their corresponding forcing mechanisms. The extent of the line indicates the area of influence, and thickness indicates relative importance to overall wave climate larger waves. In contrast, during the wet season the ITCZ moves closer to Australia, reducing the strength of the southeast trade winds and periodically altering wind direction to the north, north-east, and north-west. This thereby reduces H s and P during the wet season in the northern region. The South Pacific Convergence Zone (SPCZ) has been shown to influence the TC genesis area in the South Pacific, with cyclogenesis preferentially occurring within 10°S of the SPCZ (Vincent et al. 2011). However, further research on the strength, location, and influence of the ITCZ on wind and waves in an Australian and Coral Sea context is required.
We also determined that the central wave climate is characterised by a decreasing trend in all three wave parameters (Table 2). ENSO modulates H s , with 22% of mean H s anomalies at R2 due to ENSO and 14% of H s mean anomalies at R3 (Table 3). An analysis of Pacific wave climate by Hemer et al. (2011) found ENSO influenced wave climate on the Australian East coast, up to the southern region of the Coral Sea. The analysis performed in this study effectively shows how ENSO also influences the central region of the Coral Sea by modulating both H s and P for both mean and extreme values. During La Niña years, larger H s and increased P occur, with the opposite trend during El Niño years (Table 3). Interestingly, neither mean T z 95 or T z 95 at either R2 or R3 is correlated with ENSO, suggesting that impacts are solely related to wave height, not period. This is potentially due to more frequent TCs during La Niña phases (Jin et al. 2014), with all TC Categories producing strong winds in close proximity to the studied regions. Cyclones result in large waves that do not necessarily have large periods-albeit still larger than the T z 95 in all regions (a range of 6.3-7.1 s for R1-R4). The central region is additionally modulated by SAM, accounting for 17% and 13% of mean H s anomalies at R2 and R3, respectively (Table 3). Neither mean or extreme T z anomalies are correlated with SAM at either R2 or R3, whilst 17% and 12% of mean P anomalies are correlated with SAM, a direct relation to H s .
The southern wave climate is particularly defined by a stable wave climate, with no decadal trend detected in any wave parameter (Table 2). Furthermore, this region is significantly influenced by ENSO and SAM climate oscillations, more than the central and northern regions. A positive correlation between La Niña and mean H s and H s 95 accounts for over 40% of variation for both parameters (Table 3). SAM, whilst also modulating the wave climate, does so to a lesser extent. The positive phase of SAM results in increased mean H s , T z and P; however, there is no correlation between SAM and 95 th percentile parameters. Thus, SAM modulates the wave climate of the southern region and, however, accounts for a smaller amount of variation than ENSO, correlating with the findings of Hemer et al. (2011). We anticipate that when the La Niña phase of ENSO and the positive phase of SAM align, higher wave parameters than normal will occur in the southern region.
The climate drivers analysed in this study reveal that they play a vital role in modulating wave climate in the Coral Sea.
Interestingly, our determination of statistically significant decreasing trend in H s and H s 95 for the northern and central regions is in contrast with the findings of Young and Ribal (2019), who used similar calibrated altimeter data, in conjunction with scatterometer and radiometer data aggregated into 2°-by-2° bins. Young and Ribal (2019) found insignificant increasing trends in wave height for the majority of the Coral Sea area, for both mean and 90th percentile (H s 90 ) values, in the order of 0.33-1 cm/yr. At the southern region, several of the bins were found to have an increasing trend in altimeter H s 90 that were statistically significant, whereas the present study found no trend for either the mean H s or H s 95 . These differences are likely due to different trend and sampling methods, smaller bin sizes for the present study, and different calibration techniques. Young and Ribal (2022) determined that multi-mission altimeter datasets can be applied to ascertain trends in mean and H s 90 with an accuracy of ± 0.2 cm/yr, reducing in accuracy due to sample bias at the 99th percentile level. Therefore, it is suggested that a more robust trend analysis is an area of future study for the Coral Sea to assess the changes to future risk levels, in conjunction with assessing the influence of climate change and changing frequency and intensity of extreme events on long-term trends.
Changes to the wave climate are expected to occur due to anthropogenic climate change, with Hemer et al. (2011) noting that winter mean H s is projected to increase by 5-10% by 2100, with increases in wave period and a more southerly component for wave directions, and summer mean H s to decrease by 10-20% for the general Coral Sea area. However, changes to wave climate are expected to be highly region specific. For the south-east Australian continental margin, the mean H s is expected to decrease by 0.2 m by 2081-2100, in comparison with 1981-2000 conditions (Hemer et al. 2013). This is related to a projected storm wave energy in the region; the Coral Sea may have different climate forcings occur. Further analysis on the impact of climate change on the GBR offshore wave climate is therefore required, which may have significant consequences for the GBR ecosystem, for example, increased coral damage due to larger waves generated from the more intense, but less frequent, TC events anticipated under climate change projections.

Extreme waves in the GBR
Our analysis of TC shows that they generate large waves with long periods, thereby substantially increasing P (Table 4). Whilst the immense damage to coral reef ecosystems by TC-generated waves is widely recognised (Beeden et al. 2015;Cheal et al. 2017), the degree of ecological damage caused by different TC categories is yet to be investigated, as impacts can differ widely between reefs based on cyclone intensity, size, direction, propagation rate, and reef exposure amongst other variables. Our study of wave conditions for each category, which is the first one realised for the Coral Sea region, enables insight and recognition of the extreme and catastrophic conditions created. Conditions for TC Categories 1 and 2 were similar, with mean maximum H s substantially above the storm threshold of the Coral Sea (identified in this study) of 2.9 m. Wave conditions were significantly above modal conditions, for example, the largest Category 1 TC produced a maximum P of 570 kW, far higher than the modal P of 29 kW at the closest study site, R1. Therefore, even the lowest categories of TCs can generate extreme waves and power, likely having significant effects on ecosystems. Category 5 waves produced the largest waves, where the mean maximum H s was more than 30 times higher than modal conditions for the central region-the region of most cyclone activity.
The largest waves observed in this study were generated by TC Justin with a maximum H s of 9.6 m. We hypothesise this extremely high H s is due to a prolonged cyclone stationary period of 3 days; thus, extreme winds were focused on a small area. In addition, the altimeter tracked in close proximity to the cyclone eye and therefore obtained observations within the generation area of the cyclone. This observed value is in accordance with Vinoth and Young (2011) who estimated a 100-yrs ARI maximum wave height of 8-10 m for the region. However, as altimeter observations average wave conditions over a 7 km footprint, it is highly likely that waves larger than 9.6 m have been produced in the Coral Sea. In addition, the largest waves observed were from a Category 3 cyclone; higher categories are more likely to produce larger wave heights.

Conclusions
Our study, spanning 33 yrs of Coral Sea altimeter wave observations, shows that there are three separate wave climates offshore the GBR, each modulated by various drivers, including tropical cyclones and storms, seasonal variations, long-term trends, and climate oscillations. The highest modal wave height and power conditions occur in the southern region, decreasing in the central region and increasing again as latitude decreases to the northern region. In contrast, wave period does not significantly differ along the GBR. We find that the southern and central region wave climates are primarily modulated by ENSO, and to a lesser extent, SAM, whereas the northern region is not influenced by either climate oscillation. TCs are a major driver of extreme wave conditions, causing chaotic wave fields that can travel thousands of kilometres, and create wave heights up to at least 9.6 m offshore the GBR, over 30-fold modal conditions. Whilst this study uses available data to define wave climates for the GBR and defines three climate regions, it is important to note that as altimeters do not measure wave direction, our characterisation of the offshore GBR wave climate is not fully comprehensive. Further studies are required to (1) explain the drivers of the significant seasonality of H s in the northern region, where dry season wave heights are twice as large as the wet season wave heights, but also to (2) evaluate the role of the Intertropical Convergence Zone on wave climate seasonality and (3) assess the likely effects of anthropogenic climate change on future trends in wave climate of the region.
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