Performance Evaluation of the Newly Operational NDBC 2.1-m Hull

Candice Hall aEngineer Research and Development Center, USACE, Vicksburg, Mississippi
bDepartment of Oceanography, University of Cape Town, Cape Town, South Africa

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Robert E. Jensen aEngineer Research and Development Center, USACE, Vicksburg, Mississippi

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David W. Wang cNaval Research Laboratory, Stennis Space Center, Mississippi

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Abstract

The importance of quantifying the accuracy in wave measurements is critical to not only understand the complexities of wind-generated waves, but imperative for the interpretation of implied accuracy of the prediction systems that use these data for verification and validation. As wave measurement systems have unique collection and processing attributes that result in large accuracy ranges, this work quantifies bias that may be introduced into wave models from the newly operational NOAA National Data Buoy Center (NDBC) 2.1-m hull. Data quality consistency between the legacy NDBC 3-m aluminum hulls and the new 2.1-m hull is compared to a relative reference, and provides a standardized methodology and graphical representation template for future intrameasurement evaluations. Statistical analyses and wave spectral comparisons confirm that the wave measurements reported from the NDBC 2.1-m hulls show an increased accuracy from previously collected NDBC 3-m hull wave data for significant wave height and average wave period, while retaining consistent accuracy for directional results, purporting that hull size does not impact NDBC directional data estimates. Spectrally, the NDBC 2.1-m hulls show an improved signal-to-noise ratio, allowing for increase in energy retention in the lower-frequency spectral range, with an improved high-frequency spectral accuracy above 0.25 Hz within the short seas and wind chop wave component regions. These improvements in both NDBC bulk and spectral data accuracy provide confidence for the wave community’s use of NDBC wave data to drive wave model technologies, improvements, and validations.

Corresponding author: Candice Hall, candice.hall@usace.army.mil

Abstract

The importance of quantifying the accuracy in wave measurements is critical to not only understand the complexities of wind-generated waves, but imperative for the interpretation of implied accuracy of the prediction systems that use these data for verification and validation. As wave measurement systems have unique collection and processing attributes that result in large accuracy ranges, this work quantifies bias that may be introduced into wave models from the newly operational NOAA National Data Buoy Center (NDBC) 2.1-m hull. Data quality consistency between the legacy NDBC 3-m aluminum hulls and the new 2.1-m hull is compared to a relative reference, and provides a standardized methodology and graphical representation template for future intrameasurement evaluations. Statistical analyses and wave spectral comparisons confirm that the wave measurements reported from the NDBC 2.1-m hulls show an increased accuracy from previously collected NDBC 3-m hull wave data for significant wave height and average wave period, while retaining consistent accuracy for directional results, purporting that hull size does not impact NDBC directional data estimates. Spectrally, the NDBC 2.1-m hulls show an improved signal-to-noise ratio, allowing for increase in energy retention in the lower-frequency spectral range, with an improved high-frequency spectral accuracy above 0.25 Hz within the short seas and wind chop wave component regions. These improvements in both NDBC bulk and spectral data accuracy provide confidence for the wave community’s use of NDBC wave data to drive wave model technologies, improvements, and validations.

Corresponding author: Candice Hall, candice.hall@usace.army.mil

1. Introduction

Many researchers and engineers who are concerned with ocean conditions for construction, navigation, sediment transport, climate change, community resilience, and risk assessment studies use the National Oceanic and Atmospheric Administration (NOAA) National Data Buoy Center (NDBC) in situ operational buoy wave and wind measurements for validation and interpretation of their air–ocean–wave prediction systems (e.g., Rogers et al. 2002; Rogers and Wang 2006; Ortiz-Royero and Mercado-Irizarry 2008; Hanson et al. 2009; Jensen et al. 2012; Rogers et al. 2014; Stopa and Cheung 2014; Stopa and Mouche 2016; Bryant and Jensen 2017; Jensen et al. 2017; Rogowski et al. 2021; Jensen et al. 2021). In particular, the U.S. Army Corps of Engineers (USACE) use site specific NDBC buoy measurements to validate and verify their model and prediction products, including their long-standing Wave Information Study (WIS), their Steady State Spectral Wave (STWAVE), and their Coastal Modeling System (CMS). In addition, the USACE use NDBC wave measurements as boundary conditions to drive all offshore and nearshore wave model technologies, and as drivers for model improvements. However, all wave measurement systems have unique collection and processing attributes that result in large accuracy ranges (Cavaleri et al. 2018; Ardhuin et al. 2019). In fact, Gemmrich et al. (2011) identified buoy instrumentation and platform modifications as introducers of variability in wave measurements. Therefore, to correctly estimate the long-term U.S. wave climate, analogous wave measurements from in situ observation platforms are essential for the continued and accurate assessment of wave and ocean modeling estimates.

Since the 1980s, NDBC have routinely deployed their ocean observing systems on legacy NDBC 3-m aluminum hulls (NDBC 2016; Bouchard and Jensen 2019; NDBC 2020). Recently, Kohler et al. (2015), Bouchard et al. (2017), and Hall et al. (2018b) introduced NDBC’s new modular Self-Contained Ocean Observing Payload (SCOOP). To house this new instrumentation package, NDBC developed a 2.1-m foam hull that is specifically designed to contain the “plug and play” SCOOP (Hall et al. 2018a). In 2019 NDBC commissioned this 2.1-m foam hull into operational use, and it is this smaller, lighter hull (∼492 vs ∼1720 kg 3-m aluminum hull) that is evaluated by proxy within these wave parameter analyses.

The USACE mission is primarily concerned with the impacts of the wave climate on coastal flooding and navigation, which is critical for risk-based management, climate change and community resilience. To ensure wave data quality consistency between the legacy NDBC 3-m aluminum hulls and the newly operational NDBC 2.1-m hull, we evaluate and validate the performance of wave measurements of the newly operational NDBC 2.1-m hull, in particular, the wave energy spectra data of long-period swells (important in Pacific and Atlantic Ocean) and short-period wind seas (especially vital within the Great Lakes). Of the available 2.1-m hull evaluation sites, two were chosen to broadly highlight distinct wave environments that cover the entire frequency range of wind-generated surface gravity waves. A Great Lakes site (NDBC station 45001) showcases locally generated wind sea conditions, while a Pacific Ocean site (NDBC station 46029) captures west coast swell waves with large fetch. The paper is organized as follows. Section 2 gives a description of the evaluation methodology and statistical analyses, including a brief overview of NDBC and CDIP wave spectral parameters. In section 3, the results of the evaluation are discussed, with an overall performance determination summary in section 4.

2. Performance evaluations methods

Figure 1 depicts the hull types under evaluation: the newly operational NDBC 2.1-m foam hull; the legacy NDBC 3-m aluminum hull; and an independent reference, the Scripps Institution of Oceanography’s (SIO) Coastal Data Information Program (CDIP; http://cdip.ucsd.edu/) Datawell Waveriders (DWR). Due to nonuniformity in periods of records, as per O’Reilly et al. (1996) we evaluate the nonconcurrent NDBC 2.1- and 3-m hull performances in relation to an independent reference buoy, the CDIP DWR (ACT 2007, 2012; Luther et al. 2013; Jensen et al. 2021).

Fig. 1.
Fig. 1.

NDBC platform comparisons for (left) a 3-m aluminum discus buoy, (center) a 2.1-m foam hull SCOOP buoy, and (right) a Datawell Waverider (Datawell 2009). The orange circles highlight the location of the DDWM 3D wave system (Hall et al. 2018a; with schematic credit to Eric Gay, NDBC).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Of note is the weight and superstructure height differences between the hulls (3-m aluminum hull: ∼1724 kg and ∼5-m height; 2.1-m foam hull: ∼492 kg and ∼3.2-m height; and DWR: ∼225 kg and ∼0.5-m height). The size and shape of the buoy hull may determine the primary response nature of the buoy as either a surface-following or particle-following buoy. CDIP’s smaller size and shape results in a wave particle-following response for wave measurements, as it follows and measures the wave orbital motions (x, y, z). On the other hand, NDBC 3- and 2.1-m hulls are processed as surface-following buoys (i.e., heave, and two slopes). In an effort to isolate the hull effects, evaluation sites were selected where the target NDBC 2.1-m hull and earlier 3-m hull wave data were collected using the same directional wave measurements system, the NDBC Digital Directional Wave Module (DDWM), version 3.04, and a triaxial MicroStrain 3DM-GX1 motion sensor (herewith referred to as DDWM; Teng et al. 2009; Riley et al. 2011).

Of the available 2.1-m hull evaluation sites, two were chosen to broadly highlight distinct wave environments that cover the entire frequency range of wind-generated surface gravity waves. A Great Lakes site (NDBC station 45001 and CDIP DWR 230/WMO 45180) showcases locally generated wind sea conditions, while a Pacific Ocean site (NDBC station 46029 and CDIP DWR 179/WMO 46248) captures west coast swell waves with large fetch potential. Evaluation site details are listed in Table 1.

Table 1

NDBC and CDIP evaluation sites and deployment information. Note that 1 n mi = 1.852 km.

Table 1

NDBC deployed a 2.1-m foam hull at NDBC 45001 in May 2019, replacing the previously deployed NDBC 3-m aluminum hull. For the Pacific site, in May 2020 NDBC exchanged the 3-m aluminum hull at NDBC station 46029 with a 2.1-m foam hull, both with a seal cage adaptation, which is standard for all NDBC Pacific Ocean buoys. Collocated and concurrent Great Lakes NDBC 45001 and CDIP 230 data are available for 2017–18 for the 3-m aluminum hull, pre-2.1-m hull comparison datasets, and 2020–21 for the 2.1-m hull deployed dataset comparisons (Table 1). Similarly, 3-m aluminum hull, pre-2.1-m hull comparison datasets are available for 2011–20 for the Pacific Ocean NDBC 46029 and CDIP 179, and 2020–21 for the 2.1-m hull comparison datasets (Table 1).

As mentioned, the 2.1-m hull and earlier 3-m hull wave data at each NDBC site were collected using only the DDWM. The CDIP reference buoys compared within these analyses employ a DWR MkIII, which contain a gimballed Datawell HIPPY. The NDBC DDWM and CDIP DWR systems have different sampling strategies (Table 2). NDBC systems transmit wave messages on the hour for wave measurement data that are collected between minutes 20 and 40. DWR systems report wave messages every 30 min with wave calculations that cover a 28-min sample length. The institutional time stamps of CDIP and NDBC also differ as CDIP’s time stamp is the start of the sampling period and NDBC is the end. The DDWM utilizes 46 frequency bands (0.0325–0.4850 Hz), while the DWR MkIII exploits 64 (0.0250–0.5800 Hz). Due to the different frequency ranges, low and high DWR nondirectional spectral energy frequency bands were truncated and interpolated during spectral comparisons to remain consistent with the NDBC data.

Table 2

Wave system characteristics (adapted from Jensen et al. 2021).

Table 2

Earle et al. (1984, 1999), along with Steele et al. (1985, 1992), NDBC (2003), Riley et al. (2011), and Riley and Bouchard (2015) comprehensively described NDBC’s methodology, applied calibration techniques, and processing protocols for nondirectional and directional wave measurements. While NDBC develops and maintains their own wave systems, calibration techniques, and processing protocols, CDIP utilizes inherent Datawell methodology. Of interest here are differences in the calculation of NDBC and CDIP Datawell data products, as detailed by Earle et al. (1999) and Jensen et al. (2021).

NDBC and CDIP deliver wave elevation spectral variances, S(f), as nondirectional spectral frequency E(f) [C11(f) in NDBC nomenclature] and the four Fourier directional parameters. CDIP estimates and publishes nondirectional [a0, where a0=E(f)/π] and directional Fourier coefficients (a1, a2, b1, and b2) directly for public use, while NDBC wave systems convert these Fourier coefficients into directional functions (α1, α2) and spreading functions (r1, r2) before transmitting wave messages to shore (NDBC 2003). In this study, CDIP a0, a1,2, and b1,2 data were converted into NDBC standard nondirectional spectral energy, C11(f), α1(f), and α2(f) (mean and principal wave directions in clockwise degrees from true north), and directional spectral spreading, r1(f) and r2(f) (nondimensional first and second normalized polar coordinates of the Fourier coefficients, respectively).

On shore, both NDBC and CDIP derive significant wave height ( Hm0) from the zeroth moment (m0) of the energy spectrum, Hm0=4m0, to approximate the average of the highest 1/3 of the waves from trough to crest. NDBC and CDIP define m0=f1fu[E(f)d(f)], where spectral density E(f) is summed “over all frequency bands, from the lowest frequency f1 to the highest frequency, fu, of the nondirectional wave spectrum and d(f) is the bandwidth of each band” (NDBC 2018; CDIP 2021a). Average wave period, Ta= m0/m2 (NDBC 2018) is considered to be the zeroth moment divided by the second moment of the reported energy spectrum, where NDBC (2018) defines m2=f1fu[E(f)d(f)f2]. Conversely, CDIP calculates the average wave period as the “zeroth moment divided by the first moment of the reported energy spectrum” (CDIP 2021a). For comparative purposes during these analyses, these data were recalculated using the same NDBC moment methodology for consistency.

CDIP also publishes peak directional spread σ(fm), where fm=1/Tp, where Tp is the “period corresponding to the frequency band with the maximum value of spectral density in the nondirectional wave spectrum” (NDBC 2018) and mean wave direction at peak frequency [αm(fm)], where σ(fm)= 2{1[a12(fm)+b12(fm)]1/2} and αm(fm)={b1(fm)/a1(fm)}  (adapted from O’Reilly et al. 1996; Jensen et al. 2021). From these equations, we calculate comparative NDBC peak spread using r1 at the peak frequency: σ(fm)=2[1r1(fm)], converted to sigma from alpha, i.e., from counterclockwise from the east to the WMO (1988) convention of direction measured from true north (Earle et al. 1999; NDBC 2003). To remove shore-side processing effects and remain consistent with NDBC peak directional spread (σp) and mean wave direction at peak frequency (αm), CDIP σp and αm were recalculated as follows: α=tan1(b1/a1) and σ = [2(1 − M)]1/2, where M1=(a12+b12)1/2 (adapted from O’Reilly et al. 1996).

Although the majority of these definitions and equations are equivalent, the number of frequencies utilized by both systems are different. To remove bias, Hm0 and Ta bulk parameters were recalculated (using the formulas above) from NDBC and CDIP frequency spectral estimates, where CDIP frequencies that were truncated and interpolated to match the available NDBC frequencies. To account for directional energy captured within the higher CDIP frequencies (>0.485), directional peak spreading and mean direction (σ, θmean) were recalculated utilizing the original frequency ranges provided by the individual NDBC and CDIP sensors (Table 2). Directional peak spreading was converted from radians to degrees for plotting purposes. Outliers were removed using limits and quality controls (QC), adapted from NDBC QC protocols (NDBC 2003).

The following goodness of fit statistical analyses tested the relationship between the collocated 3-m, 2.1-m and DWR datasets: root-mean-square errors, RMSE=(1/2)r=1R(ψ^rψ)2 and bias, bias=(1/R)r=1R(ψ^rψ), where “R is the number of replications, ψ is the true population parameters, and ψ^r is the sample estimate for the rth dataset analyzed” (Sigal and Chalmers 2016). Relationship strength between the collocated samples are estimated by means of Pearson correlation coefficients, r=xy/x2y2 (Zar 1984), where 1.0 indicates a strong positive correlation. A simple linear regression method tests the trends of the datasets, Yi = A + BXi, where X is the independent variable, Y is the dependent variable, A is the intercept, and B is the slope, including an associated R2 to quantify regression variability (Zar 1984), while locally weighted scatterplot smoothing (LOWESS) regressions visually showcase a smooth curve that fits the data points, ΣkW(xk)G(xk)(ykABxk)2 for k = 1, …, N, where the robust weighting functions, W(xk) G(xk) and regression smoothing, ykABxk, are calculated for each data point (Cleveland 1979).

When considering directional results, mean wave direction at peak frequency vectors were separated into their respective north and east vector components, X = cosα1(fm) and Y = sinα1(fm) (NDBC 2003) before bias and RMSE amplitude and direction statistical calculations. Similarly for comparison plotting purposes, possible heading variations in mean wave direction at peak frequency (αm) around the 0–360 modulo cut points were also accounted for by remapping the data using their X and Y components and inferring the angles (Kelley 2018).

3. Results and discussion

Intercomparisons between systems form the basis of NDBC published accuracy standards and sensors (Bouchard et al. 2017). NDBC reporting accuracy readings (NDBC 2003, 2017) are listed as ±0.2 m for Hm0, ±1.0 s for Ta, and ±10° for mean wave direction (θm). Analyses were performed using R software (R Core Team 2021; RStudio Team 2021), and the WavEval Wave Spectra Comparison Tool, v2.0 (WavEval), a spectral comparison tool codeveloped by CDIP and the U.S. Army Corps of Engineers, Engineer Research and Development Center, Coastal and Hydraulics Laboratory (ACT 2007; Jensen et al. 2011).

For comparison purposes, Great Lakes NDBC 45001 data were subset to isolate 3- and 2.1-m hull data with their collocated and concurrent CDIP 230 DWR data (Table 1). Pacific Ocean NDBC 46029 3- and 2.1-m hull data with associated CDIP DWR 179 data were treated in the same manner (Table 1).

a. Wave height and period

Historically significant wave height ( Hm0) and average wave period (Ta) results are typically robust for NDBC wave data collection (e.g., O’Reilly et al. 1996; Bouchard et al. 2017; Hall et al. 2018a; Jensen et al. 2021). That pattern is evident within the results from this study (Table 3) as the statistical comparisons meet published NDBC accuracy standards of ±0.2 m for Hm0 and ± 1.0 s for Ta (NDBC 2003, 2017). Following the practice of O’Reilly et al. (1996), comparison Hm0 datasets return stable Pearson correlation coefficients (rhull-size) of r3-m and r2.1-m = 0.993 and reduced 2.1-m hull bias for the Great Lakes site (3-m hull observations [Obs3-m] = 4284; Obs2.1-m = 2173) when compared to collocated CDIP DWR data. The Pacific Ocean site (Table 3) also shows stable correlation coefficients with r3-m = 0.982 and r2.1-m = 0.973 and improved RMSE and bias for the 2.1-m deployment (Obs3-m = 20543; Obs2.1-m = 2645). Similarly matching Pearson correlations estimates are visible in Ta evaluations of r3-m= 0. 962 and 0.960 and r2.1-m = 0.969 and 0.959 for the same Great Lakes and Pacific Ocean datasets, respectively (Table 3).

Table 3

Goodness-of-fit statistical results between the NDBC data and the concurrent, collocated DWR data for the Great Lakes and Pacific Ocean sites. NDBC* refers to NDBC published accuracy standards (NDBC 2003, 2017).

Table 3

Of interest is the slight improvement in bias and linear regression between the Hm0 and Ta 3-m hull and subsequent 2.1-m hull analyses (Table 3; Figs. 2 and 3) when compared to collocated CDIP DWR data at both sites. The Great Lakes Hm0 bias decreased from 0.073 to 0.060 m (Table 3), and the linear regression intercept changes from −0.051 to −0.039 (slope change of 0.969 to 0.971). Variability is well explained using this linear regression model (R2 of 0.99 for both 3- and 2.1-m hull datasets). The Pacific Ocean site returns improvements in Hm0 bias from 0.070 to 0.016 m (Table 3), and Hm0 linear regression intercept of 0.966–0.986 (Table 3).

Fig. 2.
Fig. 2.

Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) Hm0 data for the (left) Great Lakes NDBC station 45001 and CDIP 230 and (right) Pacific Ocean NDBC station 46029 and CDIP 179. The 3-m (dashed) vs 2.1-m (solid) hull linear (gray) and locally weighted scatterplot smoothing (red LOWESS) regressions highlight trends. Black diamonds indicate 2.1-m hull data percentiles, and sit on a dashed gray one-to-one line for alignment reference. Blue dotted lines represent the NDBC Hm0 accuracy limits of ±0.2 m.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. 3.
Fig. 3.

Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) (top) Hm0 and (bottom) Ta percentage difference between concurrent NDBC and CDIP data, when compared to CDIP data for the (left) Great Lakes NDBC 45001 and CDIP 230 and (right) Pacific Ocean NDBC 46029 and CDIP 179; 3-m (dashed) vs 2.1-m (solid) hull locally weighted scatterplot smoothing (LOWESS; red) regressions highlight trends. All plots include a dotted gray zero line.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Figure 2 shows that the Great Lakes 3- and 2.1-m hull Hm0 both register as slighter lower than the collocated and concurrent CDIP DWR wave measurements (both integrated directly from spectral data to negate any institutional processing and quality controls edits). However, as this does not occur at the Pacific Ocean site (Fig. 2), this causation is not due to onboard sensor differences between the DWR HIPPY versus NDBC 3D-MG. As the Great Lakes is a wind-wave dominated climate, this offset is due to a hull-size sensitivity variations between the smaller 0.9-m CDIP DWR buoys and the larger NDBC 3- and 2.1-m hulls. Additionally, these effects are amplified by the NDBC processing protocols that remove any energy identified in frequencies below the sampling period specific noise frequency cutoff (approximately 0.18 Hz, ∼5 s; Riley et al. 2011). This protocol is implemented due to the amplification of low-frequency noise after integral conversion of acceleration to displacement. In fact, as a rule NDBC does not publish any peak wave period and mean wave direction data that are associated with significant wave heights below 0.25 m (NDBC 2003).

Figure 2 shows that in the Pacific Ocean, the NDBC 2.1- and 3-m Hm0 data match well to their concurrent, collocated CDIP DWR Hm0 data. Delving deeper into the Hm0 datasets collected during the 2.1-m hull deployments (Table 1), Fig. 3 shows the 3- and 2.1-m hull versus the CDIP DWR Hm0 difference versus sea state (top) and Ta difference versus average period (bottom), where both are normalized by the CDIP DWR data. The 3-m hull and 2.1-m hull versus their respective CDIP DWR datasets show similar LOWESS regression trends in both Great Lakes and the Pacific Ocean for both Hm0 and Ta, with a slight improvement in the Great Lakes Ta trend for wave periods less than 5 s. The Great Lakes Hm0 and Ta both show an increase in data scatter during low wave height and period conditions, regardless of hull type deployed. These low wave sea states are not found within the Pacific Ocean’s swell-dominated wave climate.

Figure 3 confirms that the previously identified good Hm0 correlations (Fig. 2) are associated with relatively small wave height conditions. During these sampling periods, the majority of the significant wave heights ranged between 0 and 1.5 m (∼2–5-s Ta) within the Great Lakes and between 0 and 2.5 m (∼4–8-s Ta) in the Pacific Ocean (Figs. 3).

Figure 3 highlights the importance of 2.1-m hull evaluations across multiple regions that represent different wave conditions. However, as USACE are concerned with wave development in modeling scenarios, of particular interest is the NDBC 2.1-m hull data performance when compared to the previous 3-m hull and reference CDIP DWR data across the full range of spectral frequencies. Investigating this offset further on a spectral level, bias and RMSE of average wave height as a function of wave frequency and energy on the collocated binned spectral C11(f) data (Fig. 4 and Fig. A1 in appendix A) are considered.

Fig. 4.
Fig. 4.

One month of CDIP DWR vs NDBC 3-m hull [(top left) August 2017 for the Great Lakes and (top right) August 2019 for the Pacific Ocean] and 2.1-m hull data [(bottom left) September 2020 for the Great Lakes and (bottom right) June 2021 for the Pacific Ocean] average wave height bias (in %) binned per CDIP frequency bands. Colors represent categorized bias values, where gray = ±0%–5%, blue = ±5%–10%, green = ±10%–15%, yellow = ±15%–20%, and red ≥ ±20%. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Average percent wave height bias and RMSE are binned per NDBC frequency bands, where colors represent categorized bias and RMSE values. In essence, an increase in the number of gray color bins between the 3- and 2.1-m bias plots indicates an improvement between hull types. One month’s worth of 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) were subset with their concurrent, collocated CDIP DWR data samples for testing.

These plots were created using the WavEval, v2.0 (ACT 2007; Jensen et al. 2011). WavEval applies its own interpolation process to the NDBC data to match the CDIP frequencies, which is opposite to all of the other results shown here, where CDIP frequencies were matched to the NDBC frequency data for NDBC, not CDIP, evaluation purposes.

Of note is the improvement in bias values across the spectral range between the 3-m hull and 2.1-m hull data versus their collocated and concurrent CDIP DWR values for both the Great Lakes and Pacific Ocean sites (Fig. 4). Between 0.18 Hz (the approximate frequency below which NDBC low-frequency noise filters are applied) and 0.485 (the highest frequency of NDBC data collection), the percentage of bias bins above 5% reduces from 60% to 53% in the Great Lakes (Fig. 4, left), and from 51% to 32% in the Pacific Ocean (Fig. 4, right). The scattered, higher-than-5% bias throughout the frequencies are related to slight temporal and spatial variations in the collocated datasets. The Great Lakes WavEval results highlight the increase in low-frequency energy evident within the 2.1-m hull dataset than in the 3-m hull datasets (Fig. 4). Again these results indicate a better signal-to-noise response of the 2.1-m hull. Also evident is the Pacific Ocean wave climate, where the swell energy is dominant, and the 2.1-m data match the CDIP DWR data over a broader frequency range than the 3-m data. Considering wave height RMSE, with bias removed (Fig. A1), highlights the low-frequency noise (below 0.18 Hz) disparity between the NDBC and CDIP protocols, as discussed above.

Another good test to evaluate hull performance is the agreements and deviations from unity (zero in this case) of the spectral wave energy densities (C11) and uncorrected acceleration values ( C11m) across the standard NDBC 0.020–0.485 Hz frequencies. Delving deeper into the spectral signals, mean C11 and C11m  data, with their associated ratios (red lines) were examined for August 2017 (3-m hull data) and September 2020 (2.1-m hull data) in the Great Lakes (Fig. 5), and August 2019 (3-m hull data) and June 2021 (2.1-m hull data) in the Pacific Ocean (Fig. 6). These dates were selected to incorporate a full month of data into each analysis (∼717–745 hourly samples).

Fig. 5.
Fig. 5.

The 3- and 2.1-m hull (top) mean spectral wave energy density (C11) and (bottom) mean acceleration spectra ( C11m) for the Great Lakes NDBC 45001 (orange lines) and CDIP 230 (blue lines) frequency spectra (August 2017 vs September2020). Ratios (red lines) are included for all. Vertical black dotted lines delineate the six spectral wave components, where “a” is forerunners, “b” is long swell, “c” is short swell, “d” is long sea, “e” is short seas, and “f” is wind chop.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. 6.
Fig. 6.

The 3- and 2.1-m hull (top) mean spectral wave energy density (C11) and (bottom) mean acceleration spectra ( C11m) for the Pacific Ocean NDBC 46029 (orange lines) and CDIP 179 (blue lines) frequency spectra (August 2019 vs June 2021). Ratios (red lines) are included for all. Vertical black dotted lines delineate the six spectral wave components, where “a” is forerunners, “b” is long swell, “c” is short swell, “d” is long sea, “e” is short seas, and “f” is wind chop.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

While deviations between the collocated low-frequency signals (less than 0.18 Hz) may be attributed to noise (Riley et al. 2011), the high-frequency tail of the NDBC C11 spectra (indicated by orange lines in the top plots in Figs. 5 and 6) at both locations show more agreement with the concurrent CDIP DWR frequency values (blue lines within the top plot in the figures). As these improvements are mainly evident in the short sea and wind chop spectral wave components (denoted by “e” and “f” in the figures), they indicate that the small, more lightweight 2.1-m hull is able to detect lower-frequency wave signals than the previous 3-m and larger NDBC hulls. This determination is supported by the decreased difference ratios between the NDBC and CDIP DWR data (red lines in the top figures), and is particularly enhanced in the high-frequency tail deviations within the 3- and 2.1-m hull C11m comparison plots (bottom plots in the figures). Of interest is that both sites show a 2.1-m hull C11m data unity improvement across the spectrum, even though these NDBC 3- and 2.1-m data are from different time periods. Of particular note is the reduction of noise in the lower frequencies ranges below 0.05 Hz, indicating that the 2.1-m hull is introducing less hull and sensor noise into the spectral signals. This indicates that the lighter and small 2.1-m buoy hull has a better heave acceleration response and thus has a better signal-to-noise ratio of acceleration data for low-frequency waves.

The detected shifts in the higher frequencies are clearly highlighted in 3- and 2.1-m hull deployment spectral wave components (CDIP 2021b) comparisons (Table 4 and Figs. 7 and 8 for the Great Lakes and Pacific Ocean, respectively). Short seas (0.25–0.40 Hz) and wind chop (0.40–0.50 Hz) comparisons show a visual correction in regression (gray lines) slopes after deployment of the 2.1-m hull. These trends are quantifiable in the wind-sea driven Great Lakes as stable correlation coefficients and improved bias of 0.027 from 0.035 for short seas and 0.032 from 0.060 for wind chop (Table 4).

Fig. 7.
Fig. 7.

The 3- and 2.1-m hull wave component significant wave height as calculated from spectral energy density for the Great Lakes NDBC 45001 vs CDIP DWR 230 for (top left) short swell, (top right) long sea, (bottom left) short seas, and (bottom right) wind chop. Forerunners and long swell sample sizes were too small to include here (less than 50 2.1-m hull samples). Solid gray lines represent linear regressions for the 2.1-m hull deployment data, while dashed gray lines represent linear regressions for the 3-m hull deployment data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. 8.
Fig. 8.

The 3-m and 2.1-m hull wave component significant wave height as calculated from spectral energy density for the Pacific Ocean NDBC 46029 vs CDIP DWR 179 for (top left) forerunners, (top center) long swells, (top right) short swell, (bottom left) long sea, (bottom center) short seas, and (bottom right) wind chop. Solid gray lines represent linear regressions for the 2.1-m hull deployment data, while dashed gray lines represent linear regressions for the 3-m hull deployment data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Table 4

Goodness-of-fit statistical wave component results between NDBC 3- and 2.1-m hull data and concurrent, collocated DWR data for the Great Lakes and Pacific Ocean sites.

Table 4

Increased agreements are evident in the Great Lakes (Table 4; Fig. 7) short swell (0.08–0.12 Hz) and long sea (0.12–0.25 Hz) correlation coefficients of 0.982 from 0.975 and of 0.978 from 0.975, respectively. As the Great Lakes wave climate does not include low-frequency swell data due to short fetch lengths, the Great Lakes 2.1-m evaluation data samples were not sufficient in size to evaluate forerunner (0.03–0.05 Hz) and long swell (0.05–0.08 Hz) 2.1-m hull performance (Table 4). However, the 2.1-m hull versus CDIP DWR long sea data appear more comparative than the earlier 3-m hull versus CDIP DWR long sea correlations (Fig. 8), as the 2.1-m versus DWR data show less scatter within the low wave heights (<0.25 m) than those observed within the 3-m versus DWR data. Of interest is that the Great Lakes wave component 3- and 2.1-m hull bias and RMSE results are within NDBC reported accuracy requirements of ± 0.2 m for Hm0 (NDBC 2003, 2017).

However this is not true for the Pacific Ocean wave components (Table 4; Fig. 8). RMSE results for 3-m hull long swell, short swell, and long seas versus collocated DWR tests show an exceedance of the ±0.2 m requirement at 0.208; 0.208, and 0.232 m, respectively. However, the NDBC requirement is for total significant wave height, so this is a slightly unfair assessment. In comparison, the 2.1-m hull versus CDIP DWR results do meet this NDBC requirement, with improved long swell, short well, and long seas RMSEs of 0.103, 0.147, and 0.129 m, respectively (Table 4).

Delving into the higher-frequency wave components shows a 2.1-m deployment improvement from the 3-m hull data within both correlation coefficients and bias with the collocated CDIP DWR data at the Pacific Ocean site (Table 4). Wind chop correlation coefficient results (Table 4) increased from 0.782 to 0.848, with a reduced RMSE of 0.049 m from 0.066 m, and an improved bias of 0.036 m from 0.052 m. Short seas show similar 2.1-m hull results (Table 4), with stable correlation coefficients and bias improvements of 0.027 m from 0.033 m. Reviewing the low-frequency swell data in the Pacific Ocean forerunner results (Table 4) show an improved RMSE of 0.061 m versus 0.123 m after 2.1-m hull deployment. However, a larger 2.1-m hull sample size (n = 172) is required to definitely confirm this improvement ( R2.1-m2= 0.412).

To ultimately summarize NDBC bulk parameter results as a whole, percentile nonexceedance curves show improved trends across NDBC bulk parameters ( Hm0: Fig. 9; and Ta: appendix B) across both evaluation sites. Within the Pacific Ocean, the 2.1-m hull Hm0 data reach 95% at approximately 0.38 m, while the 3-m hull data exceed 95% at 0.5 m. Hm0 remains stable within the Great Lakes, where both the 3- and 2.1-m hull Hm0 data reach 95% at approximately 0.24 m (Fig. 9). This is because fetch distances within the Great Lakes wave conditions are bounded by the size of the lakes, constraining wave height maxima and ultimately limiting the high end of the wave height distribution, as no large storm events were observed in the two datasets. Therefore, interannual wave height variations within the Great Lakes are stable and there is consistency between the nonconcurrent 2.1- and 3-m buoy data. This is not true for the Pacific Ocean, where interannual variations are based on multiple wave systems that are associated with larger fetch lengths, and thus, the high end of the wave height distributions will be affected by differences in the wave conditions from year to year. The Ta data show a very slight improvement with exceedance curves crossing the 95% threshold at approximately 0.48 s when compared to the previous 3-m hull results of 0.52 s, which is similar to the improvement within the Pacific Ocean’s Ta curves where the 95% values improves from 1.8 to 1.1 s between the hull deployments (appendix B). These exceedance curve results suggest less confidence in validations based on smaller datasets (2.1-m hull in this case), supporting an argument that any evaluation of new buoy should be treated as a long-term project, allowing time for the capture of a large range of wave conditions.

Fig. 9.
Fig. 9.

Exceedance curves for the absolute difference in Hm0 between the 3- vs 2.1-m hulls and their concurrent DWR data at the (left) Great Lakes NDBC station 45001 and (right) Pacific Ocean NDBC station 46029. The gray dotted lines represent the 95% and 99% exceedance limits.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

b. Wave direction and spread

The Great Lakes wave climate has been directly correlated to the wind directions as wind-generated seas normally are, and are spatially coherent, or follow the outline of the neighboring coastline (Lin and Resio 2001). In addition, the winds in the regions of the Great Lakes are temporally variable, which can result in translatory storm systems and shifts in wind directions between 90° and 180°. Hence the wind-driven Great Lakes wave climate typically echoes these wind shifts with oscillating wave directions, due to a strong dependency between winds and waves. This trend is evident within these reviewed Great Lakes mean wave directions (αp) as both the 3- and 2.1-m hull deployments (Table 1) have similar lobe distributions to the collocated CDIP DWR stations (Fig. 10, left). Isolating the 2.1-m hull data in Fig. 10 shows mean wave directions at peak frequency within the SE and SW quadrants, with the majority of the wave approaching from 100° to 180° and from 210° to 260°. These results are consistent with Lin and Resio (2001), and the directional lobes found at the buoy site are aligned to the primary axes for the longest fetch lengths contained in Lake Superior relative to the buoy site. Density sampling highlights the predominant Great Lakes mean wave direction at peak frequency at approximately 235° (Fig. 10) for the 2398 comparative samples collected during the 2020–21 summer and fall sampling periods (Table 1).

Fig. 10.
Fig. 10.

Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) αm data for the (left) Great Lakes NDBC station 45001 and CDIP 230 and (right) Pacific Ocean NDBC station 46029 and CDIP 179. Blue dotted lines represent the NDBC ±10° accuracy limits for direction. Green dotted lines indicate ±22.5° and ±45° limits. Both plots include a dotted gray one-to-one line.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

The Pacific Ocean evaluation site, on the other hand, is dominated by swells that originate from storms that translate across the vast expanse of the ocean basin. As expected, density sampling shows that the predominant Pacific Ocean mean wave direction at peak frequency is from the west around 280° for the 2646 comparative samples collected during the 2020–21 sampling periods (Table 1; Fig. 10, right). Of note is that the Pacific Ocean results show NDBC and CDIP processing differences when measuring multiple wave systems that contain similar peak energies in different frequency bands (Jensen et al. 2021). The offsets around 200° are primary South Pacific Ocean, low-frequency swells that are well measured by the CDIP DWR system. However, NDBC’s wave system may not be able to fully detect the low-frequency swell peaks of the multiple wave systems, meaning that this spectrum peak frequency direction may be associated with rotating high-frequency wind sea peaks. Further evaluations of the peak wave direction bias between the two systems would require isolation of the wave environment, which is beyond the scope of this work.

Reviewing the directional αp results (Table 3) show an improved directional bias of 26° for the 2.1-m hull versus CDIP DWR data, from the bias calculated using the 3-m hull versus CDIP DWR data of 52° (Obs3-m = 4666; Obs2.1-m = 2398) for the Great Lakes. Although the Pacific Ocean site does not present an improved αp bias estimate (bias3-m = 14°; bias2.1-m = 58°; Obs3-m = 20699; Obs2.1-m = 2646) after the deployment of the 2.1-m hull (Table 3), both sites show RMSE results (Table 3) as 45° across the board (Great Lakes: r3-m = 0.772; r2.1-m = 0.724; Pacific Ocean: r3-m = 0.708; r2.1-m = 0.577). However, the directional statistical results exceed NDBC’s accuracy limits of ±10° (NDBC 2003, 2017) for wave directional data at both the peak frequency, and for the directional spread around the vector mean wave direction defined at the peak frequency. The majority of the mean wave directional results remain within the ±22.5° and ±45° boundaries, designated as dashed green lines with the plots. These ±45° boundaries represent the eight primary compass directions, while the ±22.5° boundaries represent half of the eight. These directional results are consistent with other reviews of directional NDBC data (Hall et al. 2018a,b; Jensen et al. 2021).

A review of the σp comparison statistics show similar results for the 2.1-m hull and 3-m hull data versus their concurrent CDIP DWR data (Table 3). However, these less than desired results are to be expected as regression models only explain between 5% and 36% of the variation within the directional spreading datasets ( RGreatLakes230%–36% and RPacificOcean25%–6%). Figure 11 shows that directional spreading in the Great Lakes, illustrating a larger deviation in spread in smaller wave conditions, with a smaller deviation as wave size increases. This is to be expected in the Great Lakes local wind-dominated wave climate, where wave directions are highly variable in low wave height conditions. This trend is not as evident in the Pacific due to the swell-dominated wave climate, where swell is always present, even in low wave height conditions, and therefore showcase a more controlled directional wave spread. In both cases, NDBC’s peak frequency directional spread is larger than CDIP, as there is a positive bias in the NDBC spread versus the CDIP spread. Although this bias is far more consistent within the range of Hm0 found within the Pacific Ocean data. The range of directional spread deviation appears independent to the Hm0, but reviewed sample data that include consistently higher Hm0 are needed to definitely conclude this determination.

Fig. 11.
Fig. 11.

Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) σp percentage differences between concurrent NDBC and CDIP data, when compared to CDIP sea state data for the (left) Great Lakes NDBC 45001 and CDIP 230 and (right) Pacific Ocean NDBC 46029 and CDIP 179. The 3-m (dashed) vs 2.1-m (solid) hull locally weighted scatterplot smoothing (LOWESS; red) regressions highlight trends. Both plots include a dotted gray zero line.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

These results highlight that although the significant wave height and average wave period parameters show a significant improvement with the use of the 2.1-m hull, the directional parameters do not appear to be improved by the smaller hull size. To further understand these directional results, the directional spectral datasets produced by these test sites were interrogated by WavEval methodology to isolate possibly variance in the directional wave frequency data.

As with the previously described wave height WavEval methodology, evaluations compared bias and RMSEs as a function of wave frequency and energy per frequency bin for mean wave direction and directional spread (Figs. 12 and 13, Figs. A2 and A3). One month’s worth of 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) were subset with their concurrent, collocated CDIP DWR data samples for testing.

Fig. 12.
Fig. 12.

One month of CDIP DWR vs NDBC (top) 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and (bottom) 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) a1, b1 mean direction bias (in degrees) per CDIP frequency bands. Colors represent bias values, where gray = ±0°–5°, blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥ ±20°. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. 13.
Fig. 13.

One month of CDIP DWR vs NDBC (top) 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and (bottom) 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) average a1b1 spread bias (in degrees) per CDIP frequency bands. Colors represent bias values, where gray = ±0°–5°; blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥±20°. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Bearing in mind the distance between the NDBC and CDIP buoys (Great Lakes: 3 n mi; Pacific Ocean: 7 n mi; 1 n mi = 1.852 km), and the Great Lakes seasonal temporal variability (August 2017 versus September 2020), the NDBC data versus concurrent CDIP DWR data (Fig. 12) average a1 and b1 mean direction bias show a definitive improvement across all of the frequency bands for both 2.1-m hull deployment sites. Within Fig. 12, very few 0.18–0.485-Hz frequency bins return bias results that are above ±10° (NDBC directional accuracy tolerance; NDBC 2003, 2017), with a decreased from 9% to 5% of the bins recording bias above 5° in the Great Lakes, and a drop of 28%–14% of the frequency bins reporting bias above 5° in the Pacific Ocean (Fig. 12).

The Great Lakes 2.1-m hull low-frequency mean directional bias appears similar to the 3-m hull data, which is attributable to the small 3 n mi spatial difference between buoys, as well as the wind-driven directional wave climate (Fig. 12). Notice that higher than 20° bias occurs in the low-frequency bins (<0.18 Hz) in the Great Lakes samples and the 3-m hull Pacific Ocean samples, caused by the lack of resolvable energy in the low-frequency samples and the handling of low-frequency data between the two sources (Fig. 12). However, these high bias values are not present in the Pacific Ocean sites 2.1-m hull low-frequency data, meaning that the NDBC 2.1-m hull data are able to confidently mirror the nearby (7 n mi) CDIP DWR mean directional data (Fig. 12).

Mean wave directional RMSE, with bias removed (Fig. A2), appears similar in the Pacific Ocean site data, with approximately 69% and 62% of the energy across frequency bins (0.18–0.50 Hz) exhibiting RMSE between 0° and 20° for the 3- and 2.1-m hull data, respectively. RMSE results (Fig. A2) remain similar between the 3- and 2.1-m hull deployments within the Great Lakes (with most frequency bin’s bias between 0° and 20° between 0.18 and 0.50 Hz), with an increase in bias in the lower-frequency bins (<0.18 Hz). However, as mentioned this is due to spatial variability and the handling of low-frequency energy between the two sources. Both bias and RMSE results are greater than the NDBC directional accuracy limits of ±10° (NDBC 2003, 2017).

Considering mean directional spread of the directional Fourier coefficients, a1 and b1, for the NDBC data versus concurrent CDIP DWR data (Fig. 13) shows a similar bias across the frequency bands for the 3- and 2.1-m data. As before, the majority of the bins with higher bias value above 10° are detected in the frequencies below 0.18 Hz (Fig. 13). This is consistent with our previous low-frequency noise discussions, indicating an improved 2.1-m hull signal-to-noise ratio. As before, RMSE with bias removed comparisons (Fig. A3) shows a slight improvement in low frequencies at the Pacific Ocean site but otherwise results remain stable (0°–10° between 0.18 and 0.485 Hz) between the 3- and 2.1-m hull deployment data for the time period reviewed. The Great Lake RMSE results are similar, but with higher low frequencies RMSE values of 10°–15° between 0.18 and 0.22 Hz (Fig. A3). Of note is the increased amount of data for comparison in the lower frequencies within the 2.1-m hull dataset versus the earlier 3-m hull dataset, suggesting improvement in data return as the 2.1-m hull buoy is sensing an increase in low-frequency energy that is above the NDBC low-frequency filter threshold, supporting the conclusion that the 2.1-m hull buoy has an improved signal-to-noise ratio with the new 2.1-m hull. However, of note is that the reviewed Great Lakes data are temporally representing summer versus fall seasons, where the fall September data incorporate more energetic storm systems that inject low-frequency energy into the wave conditions.

Overall, NBDC 2.1-m hull directional data show a slight improvement over the previous 3-m hull deployment data. However, these data still do not appear to confirm the advertised NDBC directional accuracy limits of ±10° (NDBC 2003, 2017). The new NDBC 2.1-m hull directional data accuracy is consistent with, if not slightly better than, the previous standard NDBC 3-m hull directional data, remaining consistent with previous NDBC directional data evaluations (Hall et al. 2018a,b; Jensen et al. 2021).

4. Conclusions

Overall, the above results show that the lighter and smaller, newly operational NDBC 2.1-m hull produces significant wave height and average wave period data that more accurately compare with collocated and concurrent CDIP DWR data (improved goodness of fit results) than the previous heavier and larger NDBC 3-m hull. The NDBC 2.1-m hull directional evaluation results remain consistent with previous NDBC 3-m hull directional wave data comparisons, allowing these authors to infer that hull size does not impact NDBC directional data estimates.

Interestingly the NDBC 2.1-m hull exhibits an improved signal-to-noise ratio, especially in the lower-frequency spectral range, allowing for increase in energy retention in these frequencies. This improvement has particular relevance to USACE wave development in modeling scenarios, as swell wave development is of constant importance with regards to energy directed at coastal structures. Additionally, the NDBC 2.1-m hull provides improved high-frequency spectral results above 0.25 Hz within the short seas and wind chop wave component regions. These results are extremely relevant to USACE estimates of the long-term U.S. wave climate, a significant risk assessment consideration in all coastal research studies. Therefore, improvements within the accuracy of both NDBC bulk and spectral data allow for the wave community’s confidence in the wave measurements utilized as boundary conditions to drive nearshore wave model technologies and model improvements, as well as the wave measurements used as validation in wave models.

Future tasks include a review of the soon to be commissioned NDBC Ocean Wave Linux (OWL) system, which is a wave sensor under development at NDBC to replace their obsolete, legacy DDWM wave system. Additionally, a repeat of these evaluations should be undertaken once NDBC has deployed additional 2.1-m hulls in a broader range of wave climates, especially higher wave heights, and time allows for larger 2.1-m hull data sample sizes.

Ultimately, independent evaluations of new wave measurement technologies and instrumentation are vital for the continued development and improvement of modeling capabilities, which are essential for the protection and resilience of coastal communities and structures around the world. We have also provided a template consisting of methods, tests, and graphical presentations to follow for future intrameasurement evaluations. Regardless of their use, reliable and consistent wave measurements form the backbone of all coastal-related studies. Therefore, evaluation considerations such as the data reviewed here are required to retain high confidence throughout the work flows, from data collection agencies, to model development and risk management estimates, to basic and applied research applications that aim to save lives along our coastlines.

Acknowledgments.

The authors thank the NOAA’s National Data Buoy Center for decades of consistent data collection and for providing written permission to publish on these data. The authors would also like to thank our reviewers, especially Dr. Ian Ashton, for their invaluable review and suggestions that improved the quality of this manuscript. This work was completed as part of the Coastal and Hydraulics Laboratory’s National Coastal Wave Climate, U.S. Army Corps of Engineers Coastal Ocean Data Systems program.

Data availability statement.

The authors confirm that the data supporting the findings of this study are available within the article. Datasets analyzed during the current study are available at the National Oceanic and Atmospheric Administration (NOAA) National Data Buoy Center (NDBC) (https://www.ndbc.noaa.gov/) and the Scripps Institution of Oceanography’s (SIO) Coastal Data Information Program (CDIP) (http://cdip.ucsd.edu/).

APPENDIX A

Spectral RMSE Analysis Results

This appendix presents spectral RMSE analysis results of a month of CDIP DWR versus NDBC 3-m hull (top rows in Figs. A1A3; August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and 2.1-m hull data (bottom rows in Figs. A1A3; September 2020 for the Great Lakes and June 2021 for the Pacific Ocean). Colors represent RMSE values as indicated by the legends. Plots were created using WavEval Wave Spectra Comparison Tool, v2.0.

Fig. A1.
Fig. A1.

Wave height RMSE (in %), with bias removed, binned per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0%–10%, blue = ±10%–20%, green = ±20%–30%, yellow = ±30%–40%, and red ≥ ±40%. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. A2.
Fig. A2.

The a1b1 mean direction RMSE, with bias removed (in degrees), per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0°–10°, blue = ±10°–20°, green = ±20°–30°, yellow = ±30°–40°, and red ≥ ± 40°. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

Fig. A3.
Fig. A3.

Average a1b1 spread RMSE, with bias removed (in degrees), per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0°–5°; blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥ ±20°. White bins indicate no comparable data.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

APPENDIX B

Average Wave Period and Directional Peak Spreading Exceedance Results

This appendix presents the exceedance curve for the absolute difference in average wave period (top plots) and peak directional spread (bottom plots) between the 3- vs 2.1-m hulls and their concurrent DWR data for the Great Lakes and the Pacific Ocean (Figs. B1).

Fig. B1.
Fig. B1.

Exceedance curve for the absolute difference in (top) Ta and (bottom) σp between the 3- versus 2.1-m hulls and their concurrent DWR data at the (left) Great Lakes NDBC station 45001 and (right) Pacific Ocean NDBC station 46029. The gray dotted lines represent the 95% and 99% exceedance limits.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0172.1

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  • O’Reilly, W. C., T. H. C. Herbers, R. J. Seymour, and R. T. Guza, 1996: A comparison of directional buoy and fixed platform measurements of Pacific swell. J. Atmos. Oceanic Technol., 13, 231238, https://doi.org/10.1175/1520-0426(1996)013<0231:ACODBA>2.0.CO;2.

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  • Ortiz-Royero, J. C., and A. Mercado-Irizarry, 2008: An intercomparison of SWAN and Wavewatch III models with data from NDBC-NOAA buoys at oceanic scales. Coast. Eng. J., 50, 4773, https://doi.org/10.1142/S0578563408001739.

    • Search Google Scholar
    • Export Citation
  • R Core Team, 2021: R: A language and environment for statistical computing. R Foundation for Statistical Computing, https://www.R-project.org/.

  • Riley, R., and R. H. Bouchard, 2015: An accuracy statement for the buoy heading component of NDBC directional wave measurements. 25th Int. Ocean and Polar Engineering Conf., Kona, Hawaii, ISOPE, ISOPE-I-15-497, https://onepetro.org/ISOPEIOPEC/proceedings-abstract/ISOPE15/All-ISOPE15/ISOPE-I-15-497/14963.

  • Riley, R., C. Teng, R. Bouchard, R. Dinoso, and T. Mettlach, 2011: Enhancements to NDBC’s digital directional wave module. OCEANS’11, Waikoloa, HI, IEEE, https://doi.org/10.23919/OCEANS.2011.6107025.

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    • Search Google Scholar
    • Export Citation
  • Rogers, W. E., P. A. Hwang, and D. W. Wang, 2002: Investigation of wave growth and decay in the SWAN model: Three regional-scale applications. J. Phys. Oceanogr., 33, 366389, https://doi.org/10.1175/1520-0485(2003)033<0366:IOWGAD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rogers, W. E., J. D. Dykes, and P. A. Wittmann, 2014: US Navy global and regional wave modeling. Oceanography, 27(3), 5667, https://doi.org/10.5670/oceanog.2014.68.

    • Search Google Scholar
    • Export Citation
  • Rogowski, P., S. Merrifield, C. Collins, T. Hesser, A. Ho, R. Bucciarelli, J. Behrens, and E. Terrill, 2021: Performance assessments of hurricane wave hindcasts. J. Mar. Sci. Eng., 9, 690, https://doi.org/10.3390/jmse9070690.

    • Search Google Scholar
    • Export Citation
  • RStudio Team, 2021: RStudio: Integrated development for R. RStudio, http://www.rstudio.com/.

  • Sigal, M. J., and R. P. Chalmers, 2016: Play it again: Teaching statistics with Monte Carlo simulation. J. Stat. Educ., 24, 136156, https://doi.org/10.1080/10691898.2016.1246953.

    • Search Google Scholar
    • Export Citation
  • Steele, K. E., J. C. Lau, and Y. L. Hsu, 1985: Theory and application of calibration techniques for an NDBC directional wave measurements buoy. IEEE J. Oceanic Eng., OE-10, 382396, https://doi.org/10.1109/JOE.1985.1145116.

    • Search Google Scholar
    • Export Citation
  • Steele, K. E., C. Teng, and D. W. C. Wang, 1992: Wave direction measurements using pitch-roll buoys. Ocean Eng., 19, 349375, https://doi.org/10.1016/0029-8018(92)90035-3.

    • Search Google Scholar
    • Export Citation
  • Stopa, J. E., and K. F. Cheung, 2014: Intercomparison of wind and wave data from the ECMWF reanalysis interim and the NCEP Climate Forecast System Reanalysis. Ocean Modell., 75, 6583, https://doi.org/10.1016/j.ocemod.2013.12.006.

    • Search Google Scholar
    • Export Citation
  • Stopa, J. E., and A. Mouche, 2016: Significant wave heights from Sentinel-1 SAR: Validation and applications. J. Geophys. Res. Oceans, 122, 18271848, https://doi.org/10.1002/2016JC012364.

    • Search Google Scholar
    • Export Citation
  • Teng, C., R. Bouchard, R. Riley, T. Mettlach, R. Dinoso, and J. Chaffin, 2009: NDBC’s digital directional wave module. OCEANS 2009, Biloxi, MS, IEEE, https://doi.org/10.23919/OCEANS.2009.5422386.

  • WMO, 1988: Manual on codes. Vol. I. WMO Publ. 306, 462 pp.

  • Zar, J. H., 1984: Biostatistical Analysis. 2nd ed. Prentice-Hall, 97 pp.

  • Fig. 1.

    NDBC platform comparisons for (left) a 3-m aluminum discus buoy, (center) a 2.1-m foam hull SCOOP buoy, and (right) a Datawell Waverider (Datawell 2009). The orange circles highlight the location of the DDWM 3D wave system (Hall et al. 2018a; with schematic credit to Eric Gay, NDBC).

  • Fig. 2.

    Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) Hm0 data for the (left) Great Lakes NDBC station 45001 and CDIP 230 and (right) Pacific Ocean NDBC station 46029 and CDIP 179. The 3-m (dashed) vs 2.1-m (solid) hull linear (gray) and locally weighted scatterplot smoothing (red LOWESS) regressions highlight trends. Black diamonds indicate 2.1-m hull data percentiles, and sit on a dashed gray one-to-one line for alignment reference. Blue dotted lines represent the NDBC Hm0 accuracy limits of ±0.2 m.

  • Fig. 3.

    Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) (top) Hm0 and (bottom) Ta percentage difference between concurrent NDBC and CDIP data, when compared to CDIP data for the (left) Great Lakes NDBC 45001 and CDIP 230 and (right) Pacific Ocean NDBC 46029 and CDIP 179; 3-m (dashed) vs 2.1-m (solid) hull locally weighted scatterplot smoothing (LOWESS; red) regressions highlight trends. All plots include a dotted gray zero line.

  • Fig. 4.

    One month of CDIP DWR vs NDBC 3-m hull [(top left) August 2017 for the Great Lakes and (top right) August 2019 for the Pacific Ocean] and 2.1-m hull data [(bottom left) September 2020 for the Great Lakes and (bottom right) June 2021 for the Pacific Ocean] average wave height bias (in %) binned per CDIP frequency bands. Colors represent categorized bias values, where gray = ±0%–5%, blue = ±5%–10%, green = ±10%–15%, yellow = ±15%–20%, and red ≥ ±20%. White bins indicate no comparable data.

  • Fig. 5.

    The 3- and 2.1-m hull (top) mean spectral wave energy density (C11) and (bottom) mean acceleration spectra ( C11m) for the Great Lakes NDBC 45001 (orange lines) and CDIP 230 (blue lines) frequency spectra (August 2017 vs September2020). Ratios (red lines) are included for all. Vertical black dotted lines delineate the six spectral wave components, where “a” is forerunners, “b” is long swell, “c” is short swell, “d” is long sea, “e” is short seas, and “f” is wind chop.

  • Fig. 6.

    The 3- and 2.1-m hull (top) mean spectral wave energy density (C11) and (bottom) mean acceleration spectra ( C11m) for the Pacific Ocean NDBC 46029 (orange lines) and CDIP 179 (blue lines) frequency spectra (August 2019 vs June 2021). Ratios (red lines) are included for all. Vertical black dotted lines delineate the six spectral wave components, where “a” is forerunners, “b” is long swell, “c” is short swell, “d” is long sea, “e” is short seas, and “f” is wind chop.

  • Fig. 7.

    The 3- and 2.1-m hull wave component significant wave height as calculated from spectral energy density for the Great Lakes NDBC 45001 vs CDIP DWR 230 for (top left) short swell, (top right) long sea, (bottom left) short seas, and (bottom right) wind chop. Forerunners and long swell sample sizes were too small to include here (less than 50 2.1-m hull samples). Solid gray lines represent linear regressions for the 2.1-m hull deployment data, while dashed gray lines represent linear regressions for the 3-m hull deployment data.

  • Fig. 8.

    The 3-m and 2.1-m hull wave component significant wave height as calculated from spectral energy density for the Pacific Ocean NDBC 46029 vs CDIP DWR 179 for (top left) forerunners, (top center) long swells, (top right) short swell, (bottom left) long sea, (bottom center) short seas, and (bottom right) wind chop. Solid gray lines represent linear regressions for the 2.1-m hull deployment data, while dashed gray lines represent linear regressions for the 3-m hull deployment data.

  • Fig. 9.

    Exceedance curves for the absolute difference in Hm0 between the 3- vs 2.1-m hulls and their concurrent DWR data at the (left) Great Lakes NDBC station 45001 and (right) Pacific Ocean NDBC station 46029. The gray dotted lines represent the 95% and 99% exceedance limits.

  • Fig. 10.

    Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) αm data for the (left) Great Lakes NDBC station 45001 and CDIP 230 and (right) Pacific Ocean NDBC station 46029 and CDIP 179. Blue dotted lines represent the NDBC ±10° accuracy limits for direction. Green dotted lines indicate ±22.5° and ±45° limits. Both plots include a dotted gray one-to-one line.

  • Fig. 11.

    Scatter diagrams of the 3-m (blue points) vs 2.1-m hull (orange points) σp percentage differences between concurrent NDBC and CDIP data, when compared to CDIP sea state data for the (left) Great Lakes NDBC 45001 and CDIP 230 and (right) Pacific Ocean NDBC 46029 and CDIP 179. The 3-m (dashed) vs 2.1-m (solid) hull locally weighted scatterplot smoothing (LOWESS; red) regressions highlight trends. Both plots include a dotted gray zero line.

  • Fig. 12.

    One month of CDIP DWR vs NDBC (top) 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and (bottom) 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) a1, b1 mean direction bias (in degrees) per CDIP frequency bands. Colors represent bias values, where gray = ±0°–5°, blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥ ±20°. White bins indicate no comparable data.

  • Fig. 13.

    One month of CDIP DWR vs NDBC (top) 3-m hull (August 2017 for the Great Lakes and August 2019 for the Pacific Ocean) and (bottom) 2.1-m hull data (September 2020 for the Great Lakes and June 2021 for the Pacific Ocean) average a1b1 spread bias (in degrees) per CDIP frequency bands. Colors represent bias values, where gray = ±0°–5°; blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥±20°. White bins indicate no comparable data.

  • Fig. A1.

    Wave height RMSE (in %), with bias removed, binned per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0%–10%, blue = ±10%–20%, green = ±20%–30%, yellow = ±30%–40%, and red ≥ ±40%. White bins indicate no comparable data.

  • Fig. A2.

    The a1b1 mean direction RMSE, with bias removed (in degrees), per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0°–10°, blue = ±10°–20°, green = ±20°–30°, yellow = ±30°–40°, and red ≥ ± 40°. White bins indicate no comparable data.

  • Fig. A3.

    Average a1b1 spread RMSE, with bias removed (in degrees), per CDIP frequency bands. Colors represent categorized RMSE values, where gray = ±0°–5°; blue = ±5°–10°, green = ±10°–15°, yellow = ±15°–20°, and red ≥ ±20°. White bins indicate no comparable data.

  • Fig. B1.

    Exceedance curve for the absolute difference in (top) Ta and (bottom) σp between the 3- versus 2.1-m hulls and their concurrent DWR data at the (left) Great Lakes NDBC station 45001 and (right) Pacific Ocean NDBC station 46029. The gray dotted lines represent the 95% and 99% exceedance limits.

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