1 Introduction

Wave power measures the transport of wave energy (wave energy flux per unit of wave-crest) that is critical for shoreline evolution. Huppert et al. (2020) showed that wave power is a good predictor of how fast or slow a rocky coastline of Hawaii will erode, while Suzuki and Yoshiaki (2018) demonstrated that medium-term shoreline fluctuation is a direct result of wave power influence. Leonardi et al. (2015) postulate that variations in the background or mean wave power over the long term appear to have a greater effect on salt marsh erosion than short-term extreme wave conditions. Therefore, the background wave climate and associated long-term inter-annual wave power trends are critically important for engineers to design, protect and fortify our coastal infrastructure (USACE, 2002).

There has been a substantial effort in the impact of extreme storm events and the wave heights that affect our coastlines (Massey et al., 2011; Cialone et al., 2015; Gravens et al., 2018; Massey 2019). As multiple studies show that wave heights are increasing over time (Allan and Komar, 2000; Komar and Allan, 2007; Menéndez et al. 2008; Ruggiero et al., 2010; Young et al., 2011; Bertin et al., 2013; Panchang et al., 2013; Storlazzi et al., 2015; Jabbari et al., 2021), then it stands to reason that the power of the waves hitting our coastlines is increasing. Monitoring events and/or peak conditions from a storm might not track mean coastal damage or climate trends sufficiently, as a modest event lasting hours or days could have a larger impact on a coastline than a fast-moving extreme event. For instance, Panchang et al. (2013) and Appendini et al. (2018) found that although maximum significant wave height did not increase significantly in their independent Gulf of Mexico studies, the frequency of larger waves did. Therefore, with the added scaling effects of larger waves (with larger waves, the wavelength and period must increase), the use of only one variable (height) would lead to inaccurate results. These results necessitate an understanding of the background wave climate for determining the baseline stress levels on a coastline.

Wave data from hindcast wave models provides coverage in both space and time for long-term wave climate studies, while in situ wave data from moored buoys are often lacking due to the cost of long-term deployment and maintenance. As a result, previous studies have investigated global and local wave power using wave hindcast model outputs (Furuichi et al., 2008; Dobrynin et al., 2012; Soares et al., 2014; Reguero et al., 2015, 2019; Kamranzad et al., 2016; Mentaschi et al., 2017; Ulazia, et al., 2017; Mudelsee, 2019; Ahn and Neary, 2020). Few studies have strictly used moored buoy observation data to calculate wave power to investigate trends, due to the lack of consistent data over time (e.g. Saha et al., 2010; Reguero et al., 2019), as well as instrumentation and processing discontinuity uncertainties within observation time series data (e.g., Gemmrich et al., 2011; Young et al., 2011; Livermont et al., 2015, 2017; and Young and Ribal 2019).

Recently the United States Army Corps of Engineers (USACE) developed a self-describing Quality Controlled and Consistent (QCC) Measurement Archive (Hall and Jensen 2022) that collates historical moored buoy measurements from online NOAA National Data Buoy Center sources, removes data points from periods when the buoys were adrift or undergoing maintenance and verifies all available metadata from in-house NDBC sources for each historical data point. As this study uses these geographically cleaned data and verified metadata from the newly developed USACE QCC Measurement Archive (Hall and Jensen 2022), it confidently identifies instrumentation and system changes that occurred throughout the history of NDBC study sites. These verified metadata enable this study to be the first to offer a viable methodology to remove the observational time series data discontinuations that were highlighted by previous studies (Gemmrich et al., 2011; Young et al., 2011; Livermont et al., 2015, 2017; and Young and Ribal, 2019). Additionally, this study tests for historical shifting trends in wave power using measurement data that are interpolated for missing values and detrended for seasonality, allowing for a continuous time series of moored buoy data with no gaps and or background seasonality variance bias.

As USACE now has two unique wave data resources, the USACE QCC Measurement Archive and a long-term Wave Information Study (WIS) model hindcasts, these resources enable this unique wave climate study that uses wave data from both model and moored buoys for wave power trend validation and comparisons. Hence, this work compares long-term in situ wave power time series trends and calculations with collocated and concurrent wave model estimates of wave power, allowing for (1) the examination of long-term trends of in situ wave power time series of wave buoy data and (2) the validation of spatially and temporally comparable WIS model estimates.

The paper is organised as follows. Section 2 describes the data used within this work and provides a method for handling in situ observational calculations and discontinuities, before removing seasonality from data signals and outlining definitive statistical analyses. In Section 3.1, evaluations of the collated and concurrent observational and model wave power trends and estimates are discussed, with an overall summary in Section 5..

2 Data and methodology

This work uses the National Oceanic and Atmospheric Administration (NOAA) National Data Buoy Center (NDBC) wave data as they provide one of the longest time series of observational wave data that currently exists. Over the decades, NDBC have developed and refined new moored buoy platforms, sensors, processing protocols and modelling algorithms to improve quality in their wave measurements while responding to increasing demands for providing long-term, high-quality, continuous observational data (Earle et al., 1984, 1999; Steele et al., 1985, 1992; NDBC, 2003; Riley et al., 2011; Riley and Bouchard, 2015). However, these data are known to contain discontinuities within the long time series data, which many have identified and attempted to correct (e.g. Gemmrich et al., 2011; Young et al., 2011; Livermont et al., 2015, 2017; Young and Ribal, 2019; Hall and Jensen, 2021). This work offers a definitive solution to mitigate these discontinuities and develops the first set of wave power values that are calculated from the most accurate NDBC data to date: the newly developed USACE Quality Controlled Consistent Measurement Archive (Hall and Jensen 2022).

Wave power estimates from collated and concurrent USACE WIS datasets are used for comparative trend purposes to evaluate methodologies used within this work. The NOAA National Hurricane Center storm records and three NOAA teleconnection climate indices are included to provide context during interpretation of the observed moored buoy wave power trends.

Review sites are chosen to include a wide variety of wave environments (Fig. 1). West coast and open ocean swell wave environments with large fetch potentials are represented by the eastern Pacific Ocean and Hawaiian time series data. Locally generated wind sea conditions with localised extreme events are showcased by the Atlantic Ocean and Gulf of Mexico data. Great Lakes data that would represent locally generated wind sea conditions are ignored due to the short, summer season deployment periods of these ice-prone winter regions, which are thus riddled with large gaps in the winter wave records that cannot be supplemented. Sites were selected with deployment lengths of 30 years or longer, and deployment locations in waters that are deep enough to negate possible shallow water shoaling effects on wave power estimates. Appendix A details the reviewed NDBC and WIS sites, including their water depths and lengths of record.

Fig. 1
figure 1

NDBC and WIS study sites

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Table 1 Eastern Pacific Ocean hourly wave power (kW/m) descriptive statistics for each site (displayed from North to South) for the reviewed 40-year period
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All data manipulation and analyses were performed using R software (R Core Team, 2021; RStudio Team, 2021).

2.1 Calculating wave parameters

2.1.1 Wave power calculations

As per Resio et al. (2003), wave power (wave energy flux per metre of wave-crest length in kW/m) is calculated from Hm0 (m) and Tp (s) as \(P\approx \frac{\rho {g}^{2}}{64\pi }{H}_{m0}^{2}{T}_{p},\) where ‘ρ is the density of water (998 kg/m3) and \(g\) is the acceleration of gravity (9.81 m/s2)’ (Resio et al., 2003) for deep water waves (where water depth is greater than half the wavelength). The Resio et al. (2003) defined fresh water density constant was retained within this work due to the unavailability of the precise estimate of sea water density at each buoy location through specific regions, years and seasons. Therefore, maintaining this Resio et al. (2003) constant across all stations negates the regionally variable effects of sea water density within this work. After validation, the wave_energy function in the R software waver package (Marchand and Gill, 2018), which uses the Resio et al. (2003) equation, is used to calculate wave power.

These wave power calculations require Hm0 and Tp from the NDBC and WIS datasets. However, prior to those calculations, the NDBC moored buoy data are prepared as follows.

2.1.2 Moored NDBC buoy data

Moored buoy data were collated from the USACE QQC Measurement Archive (Hall and Jensen 2022), stored on the USACE CHL Thredds Server (USACE ERDC, 2022). Multiple works have comprehensively described NDBC’s collection methodology, applied calibration techniques and processing protocols for non-directional and directional wave measurements (e.g. Earle et al., 1984, 1999; Steele et al., 1985, 1992; NDBC, 2003; Riley et al., 2011; Riley and Bouchard, 2015). Although NDBC has predominantly used the same wave parameter definitions and equations throughout its history, shore side quality control procedures and collection platforms have advanced through the decades. For example, NDBC has historically used different wave instrumentation (detailed within Appendix B) that record spectral wave energy estimates across two frequency band ranges (NDBC 2003), a 38-band wave spectrum (0.300–0.400 Hz) and a 47-band wave spectrum (0.002–0.485 Hz). The bandwidth is a constant 0.01 Hz for the 38-band wave spectrum. However, the bandwidths of the 47-band wave spectrum are 0.005 Hz, 0.01 Hz and 0.02 Hz for low-, middle- and high-frequency regions, respectively (detailed within Appendix B, NDBC 2003, 2018a; Teng et al. 2009).

With the increase in range and bandwidth variations of the now standard 47-band wave spectrum in the 2000s (instrumentation replacement times differ across NDBC stations due to the variable maintenance schedules), the wave energy is displayed in different frequency bands between older systems and newer systems. Therefore, to account for the variations in wave energy distribution across the spectrum that would result from these different frequency ranges, available NDBC data that were collected using the 38-band wave spectrum were interpolated to match the current NDBC standard 47-band wave spectrum (Appendix C), thereby reassigning captured wave energy within comparable frequency bands. This interpolation ensures that all of the following buoy station wave height, periods and power estimates were calculated from evenly distributed wave energy across consistent frequencies throughout the evaluated time periods.

Once these frequencies were interpolated where necessary, bulk wave parameters were calculated from the now consistent NDBC non-directional spectral frequency S(f) [C11(f) in NDBC nomenclature] to mitigate for possible variance from changing shore-side processing protocols. Significant wave heights were calculated as \({H}_{m0}=4\sqrt{{m}_{0}}\). m0 is the variance of the wave displacement time series acquired during the wave acquisition period:\({m}_{0}={\sum }_{fl}^{fu}(S\left(f\right). d(f))\), ‘where the summation of spectral density, S(f), is over all frequency bands, from the lowest frequency fl to the highest frequency, fu, of the non-directional wave spectrum and d(f) is the bandwidth of each band’; NDBC, 2018b). Dominant wave period, or peak wave period, is defined as \({T}_{p}= \frac{1}{{f}_{p}}\) (NDBC, 2003), where fp represents the peak frequency band.

These frequency interpolations and subsequent recalculations of the NDBC bulk parameters identified that one of the culprits that contribute to the often discussed NDBC data discontinues (Gemmrich et al., 2011; Young et al., 2011; Livermont et al., 2015, 2017; Young and Ribal, 2019) is the historical use of these varying wave spectrum ranges. This observation is evident in the NDBC station 41,009 Tp time series data (Fig. 2, top plot), where the switch between 38-band and 47-band wave spectrum usage adds more frequency bands in the low-frequency range of the wave spectrum and thus decreases the variations of Tp on October 4, 2003 (as identified using the USACE QCC Measurement Archive). However, the bottom plot in Fig. 2 visibly shows how the interpolation of the 38-band wave spectrum into 47 frequency bands and recalculation of peak wave period alleviates this impact, removing obvious discontinuities in this NDBC data record.

Fig. 2
figure 2

Published NDBC hourly Tp (top) vs calculated hourly NDBC Tp (bottom) over time for NDBC station 41009, with orange boxes highlighting variations in peak period. Colours represent deployed hull types. Historical timelines highlighting the use of verified payload type (payload acronyms are described in Appendix B) and frequency bands are shown for NDBC station 41009. Mooring type and depth were constant for the full station deployment history. Black crosses indicate where original, hourly NDBC data are available to augment missing data within the recalculated dataset

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Another instrumentation change at NDBC station 41009 (Fig. 2) occurred on October 4, 2003: a switch from the Value Engineered Environmental Payload (VEEP) to the Acquisition and Reporting Environmental System (ARES) payload (as identified within the USACE QCC Measurement Archive), lending obscurity to our statement that Tp discontinuities are caused by different wave spectrum usage. Figure 3 showcases an example of NDBC instrumentation shifts that affected the NDBC calculated Tp at station 46029, where variations are evident between the 38-band and 47-band wave spectrum on January 3, 1997; with a random variation in Tp that is not associated with an instrumentation or system change a few months later (possibly a shore-side processing change) and between the VEEP and ARES payload switch on October 21, 2007 (as identified within the USACE QCC Measurement Archive). Figure 3 indicates that the Tp variations shift with the frequency band change in 1997, but not with the earlier switch from the Data Acquisition and Control Telemetry (DACT) payload to the VEEP on September 1, 1996. Therefore this wave spectral frequency correction utilised within this work decreases variations within the peak period, regardless of deployed NDBC instrumentation or applied shore-side processing protocols, successfully removing discontinuities in the NDBC data records used within this work.

Fig. 3
figure 3

Published NDBC hourly Tp (top) vs calculated hourly NDBC Tp (bottom) over time for NDBC station 46029, with orange boxes highlighting variations in peak period. Colours represent deployed hull types. Timelines highlighting the usage of verified payload type (payload acronyms are described in Appendix B), mooring and frequency bands are shown for NDBC station 46029. Black crosses indicate where original, hourly NDBC data are available to augment missing data within the recalculated dataset

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Apart from minimal outlier removal, no other quality control of the calculated bulk parameters was necessary, providing the first published methodology to mitigate NDBC discontinuities discussed by others using NDBC data.

Of note is that data gaps (indicated by black crosses within the bottom plots in Figs. 2 and 3) show hourly time periods where no verified spectral wave data were available for recalculation. For these instances of missing hourly spectral data and where the original hourly NDBC datasets did contain bulk parameter values (Hall and Jensen, 2021; Hall and Jensen 2022), the original NDBC bulk parameter values were inserted into the newly calculated datasets to minimise data gaps. In light of the availability of these spectral data, the minimal offsets that were introduced by augmenting the recalculated datasets with these older NDBC data (that were calculated using the 38-band wave spectrum) are deemed acceptable for this work.

2.1.2.1 NDBC buoy data gap interpolation

To investigate the temporal behaviour of the wave power at each site, a continuous time series is required for the following seasonal decomposition of wave power estimates, 90th percentile analyses, trend analyses and context comparison with climate indices. However, interpolation across large data gaps causes oversmoothing of the missing data, primarily over gaps at the start of the datasets. Therefore, NDBC datasets were subset to disregard large gaps from the early years to remove bias from the final interpolations.

Using an interpolation function within the R software package, oce (Kelley, 2018; Kelley et al., 2021), the remaining subset of data were interpolated over time to replace missing values. The function interpolates the data using the Barnes algorithm (Koch et al., 1983), which allows for the handling of sparse data periods.

For computational efficiency, the hourly datasets were aggregated to daily mean datasets. Comparisons between the interpolations of hourly versus aggregated daily mean data showed no loss in data integrity, with the aggregated daily means reducing the need for interpolation of the daily values. Aggregation to daily mean values also removes diurnal and possible tidal effects from the datasets. Therefore, aggregated daily mean values are used with confidence within these next analyses.

These interpolations were applied to all NDBC stations, with results for NDBC station 46001 from 1980 to 2021 showcased in Fig. 4, which depicts the mean daily wave power (top plot) and interpolated mean daily wave power (bottom plot) on a logarithmic scale.

Fig. 4
figure 4

Heatmaps of mean daily wave power (top) and interpolated mean daily wave power (both in kW/m and on a log10 scale) for NDBC station 46001 from 1980 to 2021

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Although Fig. 4 shows the equivalency of the interpolated data (bottom plot) with the original data (top plot), in the final time series data only the missing data within the datasets are augmented with the newly interpolated values. This practice allows for the creation of a continuous dataset that retains the integrity of the original data as much as possible. Henceforth, these new NDBC datasets that are recalculated from the consistent NDBC spectral data, and augmented with interpolated values to replace missing data, are referred to as NDBC data. These recalculated and interpolated NDBC Hm0 and Tp data are used within the wave power calculations.

2.1.3 WIS model estimates

These continuous, consistent observational wave power datasets that are created using this methodology are compared to collocated and concurrent USACE WIS wave estimates. The WIS effort was established to provide long-term wave estimates along all US coasts, including the Great Lakes, to fulfil the USACE coastal zone operations and project maintenance needs that require assessments of localised wave climates (USACE ERDC, 2020). As wave climate information is scarce due to the lack of temporal and spatial point source measurements at coastal USACE locations, the WIS generates ‘hindcast wave estimates (height, wave period and direction) and directional spectral estimates for pre-selected output locations’ (USACE ERDC, 2020). Many of these sites are intentionally collocated with the NDBC buoy locations for validation of the WIS wave estimates against wave measurements, which forms an essential part in confirming confidence in the model results.

This study inverses this model-measurement relationship by comparing these wave power measurement trends against the collocated and concurrent WIS wave power estimates. These WIS wave power estimates may be used as reference datasets within this work as they are uniformly calculated from WIS wave parameters that are computed using a consistent set of wind fields, modelling technology and general input parameters that are run on a set grid system.

The WIS uses the WAVEWATCH III® (WW3DG, 2019) model for the Pacific and Atlantic Ocean, and the WAM model (Komen et al., 1994) for the Western Alaska region and the Gulf of Mexico (USACE ERDC, 2020). Importantly, the inclusion of these different wave models denotes that a number of different spectral frequency bands (wave model frequency bands are listed in Appendix C) are used within the calculation of wave bulk parameters. As shown in the section above, the calculation of Hm0 and Tp wave parameters relies heavily on energy distribution across the spectral frequency range. As the frequency ranges differ both between the NDBC and WIS datasets and between the WIS regions, the bulk parameters used in the calculation of wave power differ in value, resulting in an offset between the comparative wave power estimates. Hence, while trends between the WIS and NDBC wave power estimates are expected to mirror each other, the magnitude of the resultant wave power will not. Without recalculating the WIS Hm0 and Tp wave parameters used in calculations of WIS wave power (beyond the scope of this work), this offset still allows for the use of the WIS estimates as a reference to evaluate the estimated NDBC wave power trends over time.

2.2 Removing seasonal effects

A seasonal component is evident within the estimated wave power across the four regions. Therefore, the data require the removal of the seasonal component to isolate changing trend signals over time. Ultimately, non-detrended and seasonally detrended daily mean wave power (kW/m) results for each region are evaluated within this work to detect changing trends over time and the importance of seasonality to the overall wave climate.

Three seasonal detrending techniques were tested to determine the most appropriate detection of variable seasonality for this application: the classical decompose method (Kendall and Stuart, 1983); a Trigonometric seasonality, Box-Cox transformation, ARMA errors, Trend and Seasonal components (TBATS) model (De Livera et al., 2011); and a Seasonal and Trend decomposition using Loess (STL) method (Cleveland et al., 1990).

The classical decompose function from the base R software stats package allows for the selection of both additive and multiplicative decomposition techniques, where additive (\({y}_{t}={S}_{t}+{T}_{t}+{R}_{t}\)) and multiplicative (\({y}_{t}={S}_{t}\times {T}_{t}\times {R}_{t})\) decomposition techniques (\({y}_{t}\) refers to the data at period \(t\), \({S}_{t}\) the seasonal component, \({T}_{t}\) is the trend-cycle component and \({R}_{t}\) the remainder, Hyndman and Athanasopoulos, 2018) are applied to the data to identify which model best suits the seasonality (day of the week, day of the month, month of the year, season or annual) of the time series data. However, classical decomposition assumes an annually repeated seasonal component and is not robust to short-term deviations from the norm (Hyndman and Athanasopoulos, 2018), which may smooth and hide an increase in storm seasonality or intensity over time. Additionally, classical decomposition does not extend trend analyses to the tails of the datasets.

To account for the complex seasonality that is crucial for these long periods of environmental time series data, an exponential smoothing state space TBATS model (tbats function: using day, month and year seasonal parameters) in the forecast package (Hyndman et al., 2021) were applied to the time series, as the model allows for seasonality changes over the period of record. Next, a STL method, which uses an additive decomposition technique to address shifts in seasonal components, outliers and change rates that reduce possible model overfitting (Hyndman and Athanasopoulos, 2018) was tested. The R software forecast package offers two STL model methods: a user-defined stl function, and a more robust mstl function (mSTL) that handles multiple seasonality.

To minimise variability in test results, the various decomposition methods were applied to hourly and aggregated daily mean datasets with minimal data gaps and rigorously scrutinised. Figure 5 provides an example (NDBC station 46029) of the wave power trends obtained from the different decomposition methods tested on the hourly data within this work. Of interest is that the classical decompose additive and multiplicative techniques returned identical trends (the NDBC and WIS additive decomposition trend lines are hidden below their associated multiplicative decomposition trend lines in Fig. 5). The manual STL model (stl function; abbreviated as STL 13 due to the use of a user-defined seasonal window = 13 in Fig. 5) under predicted trends. The mSTL trend models (black and grey in Fig. 5) appear robust enough to capture trend cycles without overfitting the model.

Fig. 5
figure 5

Decomposition methods for hourly wave power time series for NDBC station 46029

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Therefore, the mstl (multiple STL) function, which uses Friedman’s ‘super smoother’ algorithm (Friedman, J. H., 1984a, 1984b) to capture the mean, was chosen as the best method to detrend multiple seasonal periods from the data (parameters: seasonal window = 13, trend cycle window = auto) as it allows for a gradual change in possible trend cycles over time without overfitting the model. Additionally, unlike the classical decomposition methods, the mSTL function captured trend estimates across the full tails of the time series.

Of interest is that Fig. 5 clearly depicts the magnitude of the offsets between the NDBC and WIS wave power estimates as expected from the use of the non-uniform NDBC and WIS spectral ranges for bulk parameter calculations. However, the WIS and NDBC decomposition trends are in agreement within Fig. 5, as within all of the reviewed sites, definitively highlighting the accuracy of the measurement methodology used within this work, as well as the use of WIS as a stable reference for wave climate analyses.

A second methodology check that relied on these trend analyses was an evaluation of the possible loss of data integrity during aggregation of the hourly data into daily mean datasets. A review of the NDBC and WIS hourly vs aggregated daily mean decomposition trends showed no loss of data integrity. However, of interest is that the daily mean trends align more consistently with temporal-associated climate index regression trends than the hourly data, allowing for extra confidence in utilising these aggregated daily mean datasets for these wave power trend analyses.

2.3 Climate indices

In an effort to interpret the peaks and troughs in the general wave power trends observed within this work, teleconnection climate indices are incorporated for the Pacific and Atlantic Ocean regions. Trends in these climate indices provide context as to whether the wave power trends echo these climate trends after the removal of seasonal effects, or whether the wave power trends are only directly related to wind-driven storm events. Three climate indices are reviewed: the El Niño/Southern Oscillation (ENSO), a periodic fluctuation in sea surface temperature and air pressure that affects global weather (PSL, 2021; NCEI, 2021a), and two basin-specific indices: the longer-lived Pacific Decadal Oscillation (PDO) Index that affects the Pacific Basin ocean temperatures and sea-level pressures (NCEI, 2021b), and the North Atlantic Oscillation (NAO) index of sea-level pressure, which affects the intensity and location of storm tracks and the North Atlantic jet stream, and is ‘based on the surface sea-level pressure difference between the Subtropical (Azores) High and the Subpolar Low’ (NCEI, 2021c).

Odérix et al. (2020) reviewed four ENSO products and determined that the Multivariate ENSO Index Version 2 (MEI.v2) index is the product of choice to investigate global wave power. The MEI indices, which represent both oceanic and atmospheric variables, were sourced from the NOAA Physical Sciences Laboratory (https://www.psl.noaa.gov/enso/mei, downloaded on December 29, 2021). The PDO indices (Mantua, 2002) were sourced from the NCEI PDO database (NCEI, 2021b) and are based on NOAA’s extended reconstruction of SSTs (ERSST Version 5). The NAO indices were also sourced from the NCEI NAO database (NCEI, 2021c) and are based on the ‘NAO loading pattern to the daily anomaly 500 millibar height field over 0–90°N’ (NCEI, 2021c).

2.4 Statistical evaluations

The following goodness of fit statistical analyses tested the relationship amongst and between the various moored buoy test sites and the WIS model data estimations. Relationships between the co-located NDBC and WIS are assessed by Pearson correlation coefficients (\(r=\frac{\sum xy}{\sqrt{\sum {x}^{2}\sum {y}^{2}}}\); Zar, 1984), with coefficients = 1 implying a perfect fit.

Linear regressions evaluate the trends of the datasets (\({Y}_{i}=a+b{X}_{i}\), with X representing the independent variable, Y the dependent variable, a the intercept and b the slope; Zar, 1984). The curve of the data are showcased by locally weighted scatterplot smoothing (LOWESS) regressions as (\({\sum }_{k}w\left({x}_{k}\right)G\left({x}_{k}\right){\left({y}_{k}-a-b{x}_{k}\right)}^{2}\) for k = 1,…,N, with a calculation of the robust weighting functions, \(w\left({x}_{k}\right)G\left({x}_{k}\right)\) and regression smoothing, \({y}_{k}-a-b{x}_{k}\), for each data point (Cleveland, 1979).

Descriptive statistics (Zar, 1984) mean [\(\overline{X}=\frac{\sum x}{n}\), where n is the size of the sample x], median [\(Med(X)={X}_{(n+1)/2},\) if n is odd; \(Med\left(X\right)=\frac{{X}_{2}+{X}_{\left(n/2\right)+1}}{2}\) if n is even], 90th and 99th percentile [\(X=\overline{X}+Z\sigma\), where \(\sigma\) represents the standard deviation and Z = 1.282 for the 90th quantile and 2.326 for the 99th quantile] are used to investigate wave power intensity at each site over the reviewed time period. The standard error is computed as \(SE=\frac{\sigma }{\sqrt{n}}\) (Zar, 1984).

3 Trends in wave power

3.1 Regional correlations between NDBC and WIS wave power estimates

Correlations between the NDBC and WIS wave power estimates test the concurrent and collated use of these datasets for comparative wave power trend analyses. Figure 6 shows the Pearson correlation coefficients (r) of the NDBC and WIS seasonally detrended, daily mean wave power estimates for all sites across the reviewed regions. As expected, correlation coefficients (0.95, 0.78, 0.92 and 0.93 for daily mean wave power for the eastern Pacific Ocean, Hawaiian Island, Gulf of Mexico and Atlantic Ocean sites respectively) between the NDBC and WIS data show good agreement for all regions apart from the Hawaiian sites (Fig. 6).

Fig. 6
figure 6

Scatter diagrams depicting the correlations between the NDBC vs WIS seasonally detrended, daily mean wave power (kW/m) for each region. Dashed red lines indicate linear regressions, with sample size and Pearson correlation coefficients (r) listed in the top right corner. All plots include a dotted grey 1–1 line for reference

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This drop in correlation agreement within the Hawaiian sites is due to the lower efficiency of WIS to predict low wave conditions within the trade winds (Jensen, 2022, pers. comms., USACE WIS Principle Investigator). This is because WIS estimates wave conditions from large mesoscale wind conditions within that region, while Hawaii wave conditions are driven by localised weather systems that affect model estimates (Stopa et al., 2011; Li et al., 2021). During mixed wind seas and swells, WIS tends to select the swell system over the wind seas, resulting in an overestimation of the wave power estimates compared to the measurements (Jensen, 2022, pers. comms.). Additionally, these Hawaii results only represent two buoy sites (northwest and south of the Hawaiian Islands, which in the latter case is in a sheltered region), reducing any normalisation that would be introduced by additional locations; in essence, amplifying the variability signal observed at only these two specific sites. Overall, comparisons between the NDBC and WIS data at the Hawaii sites still reflect the overestimation trends observed within the eastern Pacific Ocean data comparisons, just to a greater degree.

Another heterogeneity component between the two data sources may be the coupling effects of wave-current interaction that are reported in NDBC wave measurements (Wang et al., 1994; Steele, 1997). NDBC does not rectify the net effects of surface currents within wave measurements, while WIS estimates do not contain a current component, adding to the variance between the two datasets. However, these current interactions are beyond the scope of this work and are therefore disregarded within these comparisons.

Overall, the largest daily mean wave power values were calculated for the eastern Pacific Ocean and the Hawaiian sites. Lower daily mean wave power values register at the Atlantic Ocean sites, with the lowest daily mean wave power values estimated for the Gulf of Mexico region (Fig. 6). The Atlantic Ocean WIS sites underestimate wave power when compared to collocated and concurrent NDBC wave power values, while WIS appears to be overestimating wave power within the eastern Pacific Ocean, Gulf of Mexico sites, and as expected, within the Hawaiian sites (Fig. 6). However, even with these over- and underestimates of wave power across the reviewed regions, the offsets between the NDBC and WIS decomposition trends still appear constant over time for each site (Fig. 5).

3.2 Eastern Pacific Ocean wave power

Data collected at ten eastern Pacific Ocean NDBC moored buoy sites shows maximum hourly (with seasonal effects included) intra-site wave power ranges between 416.16 kW/m (number of observations [n] = 12,766) at NDBC 46025 to 1249.94 kW/m (n = 10,307) at NDBC station 46022 (Table 2). The maximum hourly wave power at NDBC station 46025 is consistent with the expected lower wave power within the Southern California Bight, which is sheltered from North Pacific storms events, and the Channel Islands, which are not directly exposed to South Pacific and Southern Ocean swell events (Fig. 1, NDBC 46025). In contrast, a high maximum hourly wave power at NDBC station 46022 is observed in the open waters offshore of Eel River near Eureka, California (NDBC 46022).

Moored buoys are notorious for breaking adrift from their moorings during extreme weather events, compromising any wave data collected while untethered from the sea floor (Eulerian moored buoy data processing algorithms are not designed for Lagrangian movement). Therefore, of particular interest is the loss of viable maximum wave heights and periods (the building blocks of wave power) that may be recorded during these storm events. Hence, in the absence of true maximums, 90th and 99th percentile wave power values provide a more reliable comparison of wave power intensity across the individual stations. Within the reviewed eastern Pacific Ocean buoy sites (Table 1), NDBC station 46006 is subjected to the highest 90th and 99th percentile wave power due to its exposed, offshore, open ocean position.

A review of the suspect maximum recorded values and more reliable 90th and 99th percentiles across the individual eastern Pacific Ocean stations (Table 2) highlights a significant increase in wave power intensity caused by a few passing storm events. Similar wave power differences are evident in the variance between the median and mean values across the individual stations (Table 2), highlighting that the majority (median) of the wave power occurring at each site is lower than the mean. This again showcases the effects of storm events with standard deviations that are higher than both the median and mean wave power estimates. For example, NDBC station 46001 experienced mean hourly wave power of 48.29 kW/m across its lifetime, with a higher standard deviation of 63.96 kW/m, while the median wave power values at that site were far less at 25.47 kW/m (Table 2). These results indicate that the wave power distribution is highly skewed by a few intense storms. Standard errors across the datasets remain low overall (Table 2), allowing for confidence in the estimated wave power values.

Of note is that Table 2 clearly highlights the offset between the WIS and NDBC hourly wave power estimates, where 99th percentile WIS wave power estimates are consistently higher for all of the sites. The maximum wave power is only higher for the WIS sites across the northern sites (stations 46001–46006). This pattern reverses for the southern sites (stations 46022–46025), where maximum wave power is consistently lower than the NDBC estimates (Table 2).

Fig. 7
figure 7

NDBC wave power trends and overall linear regressions for the eastern Pacific Ocean (top plot), with concurrent LOWESS regressions of the reference PDO and ENSO indices for trend context (bottom plot)

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After removal of seasonal effects, NDBC daily mean wave power trends within the eastern Pacific Ocean show agreement across the sites, with the majority of the sites remaining with 20–82 kW/m (Fig. 7), and only NDBC station 46025 returning a mean daily wave power trend that oscillates around 10 kW/m (Fig. 7). Four significant peaks in 1997, 2006, 2015 and 2016 reflect the large number of tropical cyclones and depressions (19, 21, 22 and 22 storms in those years respectively: Appendix D), as recorded by the NOAA National Hurricane Center (NHC) for 1995–2021 (NHC, 2022).

Peaks in these linear regression trends appear to follow trends in both PDO and ENSO LOWESS regressions (Fig. 7), where the peaks in wave power that are evident in 1987 are associated with both the PDO and ENSO peaks. However, the ENSO peak in 1992 appears aligned with the wave power peaks observed in NDBC stations 46012 and 46013, while the wave power peaks at NDBC stations 46005 and 46002 match the PDO peak in 1993 (Fig. 7). Similar differences are observed within the 1982–1984 years, where NDBC stations 46011 and 46012 wave power trends appear to peak in time with the ENSO index, while NDBC stations 46013 and 46005 wave power trends align with the peak in the PDO index. Therefore both of these climate indices provide valuable context to the observed eastern Pacific Ocean wave power trends, especially in the absence of NHC storm counts for these earlier years.

Table 2 Eastern Pacific Ocean 40-year regression trends for each site (displayed from North to South) for non-detrended and seasonally detrended daily mean wave power (kW/m). Significant trends per year are indicated in bold (p-value < 0.05)
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As expected, linear regression trends vary across the spectrum of eastern Pacific Ocean NDBC sites (Fig. 7) as each site experiences different environmental forcing. NDBC station 46022 shows the greatest (downward) wave power trend across the stations (Table 4), which is expected as that site also exhibits the maximum wave power (Table 2).

Of note is the difference in statistical significance between the collocated and concurrent NDBC and WIS wave power trends for the reviewed sites. All but three sites (70%) show statistically significant trends (p-value less than 0.05) across the eastern Pacific Ocean NDBC stations for both the non-detrended and seasonally detrended daily mean wave power, while all WIS sites estimated significant trends (Table 2). However, all sites exhibited an acceptable NDBC-WIS Pearson correlation coefficient of 0.87 or higher (Table 2).

The relative agreement between the overall trends between each site’s wave power estimates that include seasonality (Table 4: wave power trends per year), wave power estimates that are seasonally detrended (Table 4: seasonally detrended wave power trends per year) and the associated daily slopes and intercepts suggests that within the eastern Pacific Ocean sites, statistical trend significance appears independent of seasonal effects. All trends per year are downward, apart from site 46012 (Table 4), which is offshore of Half Moon Bay, near San Francisco, CA (Fig. 1). Intriguingly, site 46013 (Fig. 1), which is just up the coast to site 46012, shows a downward trend. A trend difference of 0.098 kW/m/year separates the two NDBC stations (Table 4), even though both of these coastal shelf stations experience similar wave conditions that have developed over large distances. Overall, while seasonal detrending does not appear to affect overall statistical significance in wave power trends within the eastern Pacific Ocean, the annual wave power per year amounts varies, justifying the use of these trend analysis methodologies for coastal planning (Table 4).

In summary, these trend results show agreement with some previous wave trend estimates in slope but are not unanimous in magnitude. For example, Reguero et al. (2015) used the WaveWatchIII model to calculate eastern Pacific Ocean wave power trends of 0.5 kW/m/year (28 years of data), while Wu et al. (2018) projected wave power trends of −0.2 kW/m/year (32 years of data) that are more in agreement with our results. Of note is that these results are estimated across 1.0° × 1.0° and 1.5° × 1.0° resolution eastern Pacific Ocean model grids respectively, so are not comparable in magnitude to the discrete wave power trends per year calculated at each site within this work. Results that are comparable are the eastern Pacific Ocean buoy results within Ahn and Neary (2020) that show an inter-annual mean total wave power of − 0.13 kW/m/year (30 years of data) for NDBC buoy 46026, which, possibly due to the use of different wave power calculations, is only comparable in slope to the nearby NDBC buoy 46012 (0.20 and 0.21 kW/m/year for the non-detrended and seasonally detrended wave power respectively) reviewed within this work (Table 2). Interestingly, Ahn and Neary (2020) results are more closely aligned with the magnitude of the WIS wave power results of 0.11 and 0.12 kW/m/year for the non-detrended and seasonally detrended data respectively, although trend slopes still differ (Table 2).

3.3 Hawaii wave power

Travelling westwards into the open Pacific Ocean waters, Table 3 describes the wave power environment at the Hawaiian island review sites. Only four sites around the Hawaiian Island chain met the study parameters of deployment lengths of 30 years or longer. Additionally, NDBC stations 51003 and 51004 do not have corresponding WIS grid points for reference.

Table 3 Hawaiian Island hourly wave power (kW/m) descriptive statistics for each site (displayed from North to South) for the reviewed 36-year period
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The reviewed Hawaiian Island sites show the same maximum versus 90th and 99th percentile variability in wave power intensity (Table 3) that was observed within the eastern Pacific Ocean sites. WIS site 51001 shows an exorbitant maximum of 2212.66 kW/m (n = 8944), which does not correspond to the maximum wave power of 706.59 kW/m (n = 9488) that is identified at the collocated and concurrent NDBC station 51001 (Table 3).

NDBC station 51001 (Fig. 1) shows significantly higher values for 90–99th percentile and maximum wave power than the other Hawaiian sites, highlighting its unique location to the north of the Hawaiian Island chain with exposure to north Pacific storm swells. The rest of the reviewed Hawaiian sites fall within the southern lee of the island chains, receiving wave signals from swells originating from distant Southern Ocean storms. Again storm swell effects are evident in the standard deviations for each site across the 36-year review timeframe, with NDBC station 51001 showing a standard deviation (43.34 kW/m) of approximately twice its median wave power estimate (22.99 kW/m; Table 3). This pattern is far less evident in the southern sites, with median and standard deviations that are within relative agreement (Table 3). Again, standard errors remain low across the reviewed sites (Table 3).

This offset in northern versus southern wave power values are echoed within the overall trends of the time series data (Fig. 8), where mean daily wave power for NDBC station 51001 registers higher (30–50 kW/m) than the rest of the Hawaiian sites (20–40 kW/m). The peak in mean daily wave power during 1997 (Fig. 8) mirrors the nine tropical cyclones and depressions that were recorded by the NHC within the Central Pacific Ocean during that year (Appendix D). Similarly, the 2015 peak in wave power reflects the five tropical cyclones and depressions listed by the NHC (Appendix D) for the region. Again, trends in the wave power (kW/m) show a temporal agreement with the PDO and ENSO LOWESS regression trends, where both climate trends match peaks in NDBC 51002 and 51003 wave power in 1987, and again in 1997 and 2010 (Fig. 8). The peaks in the PDO index appear reflected within the 1993 peaks in wave power at NDBC station 51004, and the 2001 peaks across all of the reviewed NDBC sites (Fig. 8). A smaller peak in 2012 is evident in wave power at NDBC station 51004 that coincides with a peak in the ENSO index (Fig. 8), justifying the use of both climate indices to provide context to the Hawaiian Island sites.

Fig. 8
figure 8

NDBC wave power trends and overall linear regressions for Hawaii (top plot), with concurrent LOWESS regressions of the reference PDO and ENSO indices for trend context (bottom plot)

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The disagreement in NDBC and WIS wave trends for site 51001 are clearly evident in the low 0.78 and 0.67 Pearson correlation coefficients for non-detrended and seasonally detrended data respectively (Table 4). These results show that all trends, both non-detrended and seasonally detrended data, are downward at the Hawaiian sites (Table 4), indicating that wave power has decreased slightly over the reviewed 36-year time period. Again, trend statistical significance (p-value less than 0.05) appears independent of seasonal effects, with 100% of the reviewed sites showing a downward trend in wave power over the 36-year time period (Table 4). These results agree in slope but are not comparable in magnitude (with − 1.16 and − 1.15 kW/m/year for non-detrended and seasonally detrended wave power) with Ahn and Neary’s (2020) recent 30-year review, which estimated an inter-annual mean total wave power of − 0.25 kW/m/year for NDBC station 51001.

Table 4 Hawaiian Island 36-year regression trends for each site (displayed from North to South) for non-detrended and seasonally detrended daily mean wave power (kW/m). Significant trends per year are indicated in bold (p-value < 0.05)
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3.4 Atlantic Ocean wave power

Results show less wave power within the Atlantic Ocean than in the eastern Pacific Ocean, with a maximum hourly intra-site wave power range between 384.47 kW/m (n = 9453) at NDBC station 44014, to 906.36 kW/m (n = 10,132) at NDBC station 41002 (Table 5). NDBC station 44011, which is subjected to frequent Nor’easter storms, appears the most energetic over the reviewed 40-year period, with 90th and 99th percentile of the waves experienced by that station measuring wave power of 59.01 and 199.88 kW/m.

Of note is that the mean and median wave power values recorded within the Atlantic Ocean are approximately five times lower than those observed within the eastern Pacific Ocean. These results are due to the difference in storm systems that affect the two areas, as well as the position of the buoys relative to the open ocean within each region, both affecting the Tp values that feed into the wave power estimations.

Table 5 Atlantic Ocean hourly wave power (kW/m) descriptive statistics for each site (displayed from North to South) for the reviewed 40-year period
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Standard deviations across a number of the reviewed Atlantic sites are generally comparable to the 90th percentile wave power estimates, and not the median or mean wave power calculations (Table 5). These results are due to the locally generated wind sea wave conditions with localised extreme events that are experienced at these sites. Standard errors across the reviewed sites remain low (Table 5), again allowing for confidence in these calculations.

As at the eastern Pacific Ocean sites, linear regression trends within the Atlantic Ocean vary across the spectrum of NDBC sites (Fig. 9) with environmental forcing variations. After removal of seasonal effects, NDBC daily mean wave power trends, ranging from 5 to 35 kW/m within the Atlantic Ocean, show agreement in mean daily wave power peaks and troughs, if not wave power magnitude, across each site (Fig. 9).

Fig. 9
figure 9

NDBC wave power trends for the Atlantic Ocean, with concurrent LOWESS regressions of the reference NAO and ENSO indices for trend context (bottom plot)

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These wave power trends appear to follow trends in both NAO and ENSO LOWESS regressions, where peaks are evident within both climate indices and NDBC stations 44005, 41001 and 41002 between 1982 and 1984 (Fig. 9). Trends in wave power peaks at NDBC stations 41001 and 41002 correspond to NAO peaks in 1989, while peaks at all but one of the NDBC stations match the NAO peak in 1999 (Fig. 9). Peaks in wave power at NDBC stations 44008, 44011, 41001 and 41002 appear aligned with a peak in ENSO trends in 1986–1987, with all NDBC stations showing a peak in line with the ENSO peak in the 1998 timeframe, and again in 2015 (Fig. 9).

Of interest is the universal peak in wave power across the NDBC station within 2005 that does not correspond to a peak in the NAO or ENSO indices (Fig. 9). This peak, however, clearly reflects the extremely active 2005 hurricane season that the Atlantic Ocean experienced (Appendix D), where the NHC recorded 31 tropical cyclones and depressions for the area. This seasonal intensity is only matched within the Atlantic Ocean by the recent 2020 hurricane season, which, unfortunately, is not fully captured within our dataset (Fig. 9). However, the 1995, 2003, 2010, 2011 and 2019 hurricane seasons all registered 20 or more storm events (NHC 2022; Appendix D), which are echoed in the trend peaks within Fig. 9.

The overarching objective of these plots is to notice that a number of NDBC stations are showing an upward linear regression trend across the 40-year reviewed period (Fig. 9), deviating from the previous, almost universal downward linear regression trends observed within the eastern Pacific Ocean. In fact, four (NDBC stations 41009, 44008, 44013 and 44014) of the ten Atlantic sites show upward trends for both seasonal and seasonally detrended trends over the time period (Fig. 9; Table 6), which are consistent with Ahn and Neary’s (2020) Atlantic moored buoy inter-annual mean total wave power of 0.02 kW/m/year for NDBC station 44025 (a site not reviewed within this study due to a deployment period of less than 30 years). Interestingly, NDBC stations 44008 (0.175 kW/m/year) and 44011 (− 0.025 kW/m/year), both situated on the coastal shelf in relatively close proximity (Fig. 1), return opposite non-detrended wave power trend results (Table 6).

All but three NDBC stations show upward trends that are statistically significant (p-value less than 0.05), with all of the WIS sites estimating upward trends for wave power that is seasonally detrended (Table 6). As expected with the offset in wave power, a higher number of WIS sites return significant trends; however, all sites exhibited a good NDBC-WIS Pearson correlation coefficient of 0.91 or higher (Table 2). No site-specific correlations for latitudinal (North to South) or longitudinal (East to West) wave power trends were detected.

Table 6 Atlantic Ocean 40-year regression trends for each site (displayed from North to South) for non-detrended and seasonally detrended daily mean wave power (kW/m). Significant trends per year are indicated in bold (p-value < 0.05)
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3.5 Gulf of Mexico wave power

Of the reviewed regions and even with its famous hurricane-prone reputation, the Gulf of Mexico sites captures the least amount of wave power overall, with hourly maximums ranging from a low of 144.89 kW/m (n = 8659) at NDBC station 42019, to a high of 664 kW/m (n = 11,941) at NDBC station 42003 for the 39-year review period (Table 7). However, a large portion of the wave power is captured within the 99th percentile, which reaches a Gulf of Mexico maximum of 59.84 kW/m (n = 13,146) at NDBC station 42002 (Table 7). Within this region, median hourly wave power values are predominantly lower than the other regions, ranging between 2.29 kW/m (n = 11,941) at NDBC station 42003 (even though this station exhibits the highest maximum wave power within the region) to 4.02 kW/m (n = 9097) at NDBC station 42020 (Table 7).

Table 7 Gulf of Mexico hourly wave power (kW/m) descriptive statistics for each site (displayed from North to South, then West to East) for the reviewed 39-year period
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These results are due to the smaller Gulf of Mexico body of water, where the background wave climate is predominantly composed of locally generated wind sea conditions, and minimal swells entering into the system through the Yucatan Channel or Florida Straits. NDBC station 42003 (Fig. 1) is the closest reviewed station to these channels to the Atlantic Ocean and is situated within the location of the oscillating Gulf Loop Current (Maul, 1977; Oey et al., 2005). NDBC stations 42020 and 42019 (Fig. 1) are on the continental shelf in the shadow of the US land mass that reduces open water area for local wind-wave development, which explains their minimal wave power values, although they are exposed to easterly and south-easterly wind-wave growth. NDBC station 42001 and 42002 (Fig. 1) are subjected to Loop Current eddies that break away from the main Loop Current and propagate westwards (Maul, 1977; Oey et al., 2005), introducing wave energy into the system through their clockwise rotations.

These various land and oceanographic influences on the wave climate within the Gulf of Mexico are evident in the mean daily wave power trends and linear regression trends over time (Fig. 10). However, significant hurricane events, Hurricane Katrina (August 2005; Knabb, 2005); Hurricane Rita (September 2005; NHC, 2022); and Hurricane Wilma (October 2005; NHC, 2022), passed over NDBC station 42003 with enough wave power to ensure their signals are represented in the seasonally detrended mean daily wave power (orange box in Fig. 10). Here the mean daily seasonally detrended wave power reaches 24 kW/m, far exceeding the background mean daily wave power trends that range within 5–12 kW/m for the then (prior to 2020) record-breaking 2005 hurricane season (Fig. 10). Of note is that the data signal evident for September 2005 is interpolated NDBC data, as the mooring at NDBC station 42,003 failed during Hurricane Katrina (August 28, 2005), before NDBC redeployment on October 6, 2005. These results provide yet another validation of the data methodology applied for these analyses.

Fig. 10
figure 10

NDBC wave power trends for the Gulf of Mexico. Peaks within the wave power trends did not appear similar to trends within the climate indices, and so are not included. The dramatic peak experienced during 2005 at NDBC station 42003 represents the increase in wave power as Hurricane Katrina moved over the buoy (orange box)

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The lower background wave power estimates are echoed within the non-detrended and seasonally detrended daily mean wave power regression trends in Table 8, where only one NDBC station (42019) shows both a statistically significant non-detrended (− 0.030 kW/m/year; n = 10,228) and seasonally detrended (− 0.029 kW/m/year) trend, and only one NDBC station (42001) shows a significant seasonally detrended trend (− 0.016 kW/m/year; n = 13,880). These results show the benefits of reviewing variability between non-detrended and seasonally detrended wave power trends. Of note is that these smaller wave power trends show relative agreement with Ahn and Neary’s (2020) NDBC station 42040 inter-annual mean total wave power results of 0.04 kW/m/year.

Table 8 Gulf of Mexico 39-year regression trends for each site (displayed from North to South) for non-detrended and seasonally detrended daily mean wave power (kW/m). Significant trends per year are indicated in bold (p-value < 0.05)
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Overall, of the five reviewed Gulf of Mexico NDBC stations, three stations returned downward mean power trends, and two stations returned upward trends per year (Table 8), regardless of seasonality. NDBC and WIS trends and slopes differ at all the sites with downward trends per year at the collocated locations, due to the low wave energy environment. However, all sites exhibited reasonable NDBC-WIS Pearson correlation coefficients of 0.85 or higher (Table 8), even with the varying directional slope trends.

3.6 Regional 90% wave power

For coastal engineering and planning purposes (Forte et al., 2012), the non-detrended 90th percentile wave power results were annually aggregated across each region to isolate maximum values within the Atlantic Ocean, Gulf of Mexico, eastern Pacific Ocean and Hawaii (Fig. 11). These results show that those considering baseline wave power conditions within the eastern Pacific Ocean should expect the maximum 90th percentile of non-detrended for season wave power values to range between 414 and 1937 kW/m (n = 43 years), with standard errors (SE) from 45 to 175 kW/m respectively across the eastern Pacific Ocean NDBC stations (Fig. 11, top plot). Within the Atlantic Ocean, non-detrended for season wave power values are less intense, with maximum 90th percentile values ranging between 312 and 1551 kW/m (SE: 21–196 kW/m; n = 42 years) across the NDBC sites (Fig. 11, top plot). Moving further down the scale in wave power intensity, the Hawaiian NDBC sites (Fig. 11, top plot) show maximum 90th percentiles of non-detrended for season wave power values that range between 180 and 803 kW/m (SE: 12–171 kW/m; n = 37 years). Finally, the least intense reviewed wave power region, the Gulf of Mexico NDBC sites (Fig. 11, top plot), have recorded a maximum 90th percentile of non-detrended for season wave power values that range between 66 and 934 kW/m (SE: 3–148 kW/m; n = 41 years). Interestingly, the 2005 Gulf of Mexico hurricane season is represented as above the norm within the annual maximum 90th percentile (Fig. 11).

Fig. 11
figure 11

Spatial and temporal variability in annually aggregated, non-detrended, maximum NDBC (top plot) and WIS (bottom plot) 90th percentile wave power (kW/m) across the Atlantic Ocean, Gulf of Mexico, eastern Pacific Ocean and Hawaii, with error bars representing the standard error

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The WIS non-detrended for season, maximum 90th percentile wave power shows a larger range of 471–2311 kW/m (SE: 45–206 kW/m; n = 41 years) for the eastern Pacific Ocean sites, 240–1492 kW/m (SE: 20–155 kW/m; n = 41 years) for the Atlantic Ocean sites, 252–2200 kW/m (SE: 64–922 kW/m; n = 36 years) for the Hawaiian sites, and 47–923 kW/m (SE: 5–188 kW/m; n = 40 years) for the Gulf of Mexico sites. As before, the peaks of NDBC and WIS wave power estimates show agreement in the peaks over time, but magnitude differences between the two dataset persist within these results.

Therefore, the spatial and temporal variability between the NDBC and the WIS wave power estimates are evidenced by higher WIS wave power ranges for the eastern Pacific Ocean and Hawaiian Island sites, and comparable maximum 90th percentile wave power ranges for the Atlantic and Gulf of Mexico sites. Apart from the Hawaiian sites, standard errors appear relatively similar between the NDBC and the WIS wave power ranges. The annual maximum 90th percentile per region has a tendency to overshadow the individual buoy results, necessitating the calculation of site-specific wave power estimates for accurate assessments. However, while the investigation of wave power potential at individual sites requires a localised wave climate study for accurate planning and engineering purposes, these overall baseline wave power estimates will assist in initial project designs and development within each of the four regions.

4 Summary

In summary, buoy measurement data may be used to calculate wave power trends over time. Additionally, moored buoy wave power data are comparable with wave model wave power estimates; both showing that wave power trends are not increasing over time as appreciably as significant wave heights. Overall, the majority of the eastern Pacific Ocean and Hawaii wave power trends are downward, with mixed slope wave power trends apparent within the Atlantic Ocean and the Gulf of Mexico. As there is a noticeable variability in the trend direction within each reviewed region, site specific trends should not be generalised to represent a large region.

Wave power estimates differ from region to region due to area-specific wave conditions, with the eastern Pacific Ocean ranking as the more energetic of the regions with respect to wave power. After ranking by maximum wave power, 60% of the top ten stations are located along the eastern Pacific Ocean coastline. The Atlantic Ocean registers as the second most energetic coastline within these reviewed sites, with Hawaii logging in at third place. The Gulf of Mexico contains the least amount of wave power with these regions, although the Gulf of Mexico wave power trends clearly highlight extreme weather events that affect the region.

The higher wave power values that are observed within the eastern Pacific Ocean are attributed to the swell-dominated, longer Tp conditions that those sites are exposed to. These conditions form from a combination of North Pacific storms that pass through between autumn and spring, as well as the southern swells from the South Pacific and the Southern Ocean that penetrate the region within the summer months. The Atlantic Ocean experiences lower Tp conditions due to a predominant wave climate of local wind seas with following swells from Nor’easters. For the southern Atlantic Ocean locations (south of Cape Hatteras), tropical cyclone activity is evident in spatially variable wave power values that are a factor of five lower than those observed within the eastern Pacific. Within the Hawaiian region, the northern versus southern sites showed a difference in wave power magnitude (higher in the north), highlighting the effect of the northern site’s exposure to North Pacific storm swells, while the rest of the reviewed Hawaiian sites experienced central Pacific and Southern Ocean swell signals. While the Gulf of Mexico records the lowest wave power values across the four reviewed regions due to its wind sea conditions and smaller area, the net impact of extreme events is evident within the background wave power estimates.

Overall, all of the reviewed regions produced daily mean wave power trends that show associations with extreme tropical weather events that were recorded by the NHC (1995–2021). Peaks in wave power trends throughout the eastern Pacific Ocean, Hawaiian and Atlantic Ocean sites appear to follow trends in both concurrent and variable PDO, NAO and ENSO LOWESS regressions. However, correlation does not infer causation and without in-depth analyses into the relationships between these wave power trends, and the reviewed climate indices, no definitive results are available here.

Finally, as the majority of wave power trend analyses and coastal engineering wave climate risk assessments are performed using wave model datasets, one of the objectives of this work was to quantitatively assess the differences between these model and observational data sources. Results show significant differences between the NDBC moored buoy and wave model wave power results that highlight the importance of using site specific results to investigate wave power within regions. These NDBC and WIS differences may be due to the different spectral-band frequency ranges that are used to calculate the bulk wave parameters required for these wave power calculations. They also highlight the importance of using wave power over individual bulk parameters to evaluate the performance of the WIS modelling technology. As this is the first study to use wave power as a metric to evaluate wave model results, there is reason for additional investigation to identify potential deficiencies in wind forcing or modelling technology.

In conclusion, moored buoy data are successfully accessed to investigate wave power trends within four coastal regions around the US. While observational and model results are relatively similar, the moored buoy data presents smaller wave power ranges for two of the four regions, suggesting that observational data are essential in local wave climate studies to ensure accurate estimates for coastal planners and engineers.