Performance evaluation of an offshore wave measurement buoy in monochromatic waves

TL;DR

This study quantifies the Datawell DWR-MkIII buoy’s wave-elevation and energy-flux measurement performance under controlled monochromatic forcing on the large-amplitude motion platform, treating the buoy as an ideal wave follower and validating commanded motions with an optical system. A Bayesian optimization framework designs the experiment across the buoy’s nominal period range (roughly $1.6$–$30$ s), and results are propagated to four energy-flux estimators, including a frequency-domain method and three time-domain methods. The analysis identifies two dominant error regimes: short periods $T_m<5$ s affected by sub-Nyquist sampling and long periods $T_m>25$ s dominated by elevation attenuation and processing, yielding energy-flux errors up to and beyond $100\%$ in the short range and tens of percent in the long range. Field-data tests with three CDIP sites show the IEC-reported frequency-domain baseline is generally robust within about $6\%$, but method-dependent biases exist (e.g., Hilbert underestimates by $\sim$6.9–14.4%), highlighting the need for uncertainty quantification and potential standards refinements.

Abstract

The accurate measurement of waves underpins marine energy resource characterization, device design, and project development. Datawell wave buoys are widely deployed around the world and have long served as a trusted standard for wave measurements. We quantify the measurement performance, including wave elevation and energy flux estimation, of a Datawell DWR-MkIII buoy using prescribed monochromatic heave motions on a large-amplitude six-degree-of-freedom motion platform at the National Laboratory of the Rockies, assuming the buoy behaves as an ideal wave follower. Commanded motions were validated with an optical motion tracking system while buoy elevation and raw acceleration were recorded. Wave elevations were propagated to wave energy flux estimation using four methods, including one frequency-domain method and three time-domain methods. The Bayesian optimization was applied for design of experiments, and records from three test sites were also applied and evaluated in the present study. Results show two error regions within the nominal period range of 1.6s to 30s}. For wave periods between 5s and 25s, the buoy provides accurate wave height measurements. For short periods less than 5s, the 1.28Hz sampling frequency induces sub-Nyquist artifacts that bias elevation and can drive maximum energy flux estimation errors above 100%. For long periods exceeding 25s, the buoy reported elevation is underpredicted with error depending on period but relatively independent of wave height, with maximum wave height and wave energy flux errors reaching 64% and 87%, respectively. The analysis of field data also indicates that the currently recommended method for estimating wave energy flux may underestimate the wave energy flux.

Figures (14)

• Figure 1: Ferris-wheel buoy calibration device. The buoy is fixed in the apparatus and forced to move through a circular trajectory, simulating its response.
• Figure 2: Experimental setup: (a) Diagram of experimental system and coordinate definition. Two different coordinates are used in the present study with $O-XYZ$ as LAMP motion coordinate and $O^\prime-X^\prime Y^\prime Z^\prime$ as buoy motion coordinate. (b) Overview of experimental setup. Buoy is fixed in LAMP system through a hex support frame.
• Figure 3: Definition of wave parameters. $h$ is the water depth, $L$ is the wave length, $H$ is the wave height, and $\eta(x,t)$ is the wave elevation.
• Figure 4: Distribution of the wave height measurement error $\sigma$ over the amplitudes $A_m$ and periods $T_m$. Each dot corresponds to one test condition, and the color indicates the value of $\sigma$ shown in the colorbar.
• Figure 5: Contour and scatter results of the wave height measurement error $\sigma$: (a) Contour distribution of wave height measurement $\sigma$ over $T_m$ and $A_m$; (b) variation of $\sigma$ with $T_m$ for several amplitudes $A_m$. The error increases in both short- and long-period ranges, consistent with the discrete results shown in \ref{['heightall']}.