Pitch-roll Buoy Research Articles

Uncertainty of Wave Spectral Shape and Parameters Associated with the Spectral Estimation

The uncertainty in estimating the wave spectrum from the records of wave elevation by heave–pitch–roll buoys is studied, considering the effects of the estimation method and the spectral resolution adopted in the process. This investigation utilizes measurements from a wave buoy moored in deep water in the South Atlantic Ocean. First, the spectra are computed using the autocorrelation function and the direct Fourier method. Second, the spectral resolution is tested in terms of degrees of freedom. The degrees of freedom are varied, and the resulting spectra and integrated parameters are computed, showing significant variability. A simple and robust methodology for determining the wave spectrum is suggested, which involves calculating the average energy density in each frequency band. The results of this methodology reduce the variability of the estimated parameters, improving overall accuracy while preserving frequency resolution, which is crucial in complex sea states. Additionally, to demonstrate the feasibility of the implemented approach, the final spectrum is fitted using an empirical model ideal for that type of spectrum. Finally, the performance and the goodness of the fit process for the final averaged curve are checked by widely used statistical metrics, such as R2 = 0.97 and root mean square error = 0.49.

Directional Surface Wave Spectra from Point Measurements of Height and Slope

AbstractWe describe here a method for recovering directional ocean surface wave spectra obtained from height and slope measurements made over a small area, the iterative deconvolution method (IDM). We show that IDM is a more reliable method for estimating directional wave spectra than more common spectral estimation techniques by comparing it with the widely used maximum entropy method (MEM). IDM is based on the observation that pitch–roll buoys produce directional spectra that are the true spectra convolved with an angular windowing function and are therefore much broader than the true spectra. We test IDM against simulated data and find that it does a better job of retrieving the known input spectra than does MEM, which often produces false double peaks or incorrect angular widths. We compare IDM recoveries to spectra obtained using a nonstandard processing technique, the wavelet directional method (WDM) on data from a compact array of wave staffs on Lake Ontario. We find that IDM produces directional wave spectra very nearly identical to those obtained using WDM, verifying both techniques. Finally, we processed standard NDBC buoy directional spectra and showed that IDM recovers ocean wave spectra that narrow in the Strait of Juan de Fuca and that follow a changing wind in the expected manner. Neither of these phenomena are reliably obtained using MEM due to its tendency to produce false bimodal peaks and peaks that are too narrow.

Question of the pitch-roll buoy response to ocean waves as a simple harmonic oscillator?

The assumption that the East and North deck slopes of a pitch–roll buoy respond to East and North sea slopes as simple harmonic oscillators is routinely made by the National Data Buoy Center (NDBC) and others producing directional wave data. Although directional wave data derived with this assumption usually appear to be of good quality, the validity of the assumption has not previously been more directly demonstrated. In this paper, a method is proposed to judge the validity of the assumption for any set of time series records of buoy angular motion. The proposed method is applied to 200 record sets taken by an NDBC buoy located at ocean station 46024, and to five record sets taken by another NDBC buoy at 46051. For the 46024 data, it was demonstrated that the simple harmonic oscillator assumption was near perfectly valid. For the smaller 46051 data set, the simple harmonic oscillator assumption was shown to be slightly less valid.

Pitch-roll buoy mean wave directions from heave acceleration, bow magnetism, and starboard magnetism

This paper describes the refinement of a previously published procedure for estimating Mean Wave Direction using azimuth, pitch, and roll derived from only the bow and starboard components of the earth magnetic field. To demonstrate the effectiveness of this refined procedure, it is applied to sensor time series records taken over a single twenty-minute period aboard a pitch-roll buoy, and results are presented. On the assumption that the method will be verified by additional data, practical means to apply it operationally are outlined.

Evolution of the Bimodal Directional Distribution of Ocean Waves*

Abstract Recent results of numerical wave models have shown that the presence of a bimodal directional spreading is a robust feature at wavenumbers above the spectral peak. This directional bimodality is controlled mainly by directional transfer of energy through nonlinear wave–wave interactions. The bimodal feature has also been observed in the directional spectra derived from the spatial topography of ocean surface waves acquired by stereo-photography, image radars, and an airborne scanning lidar system. In this study, a comprehensive data analysis of the evolution of the wave directional distribution during two active wave growth periods in Lake Michigan is conducted. The wind and wave measurements are acquired by two heave–pitch–roll buoys moored at a nearshore and an offshore station. An empirical method averaging the results of the maximum likelihood method and maximum entropy method is used to estimate the directional distribution from buoy measurements. The study shows that the bimodal distributio...

Use of advanced directional wave spectra analysis methods

Frequency-dependent cross-spectral parameters for pitch-roll buoy data and parameters that describe directional wave spectra based on a directional Fourier series are developed by the National Data Buoy Center (NDBC) and other organizations that collect wave data. The World Meteorological Organization (WMO) specifies wave data product formats in its Wave Observation (FM 65 WAVEOB) code. Other organizations, such as the US Army Corps of Engineers Field Wave Gaging Program (FWGP), have similar specifications. A directional Fourier series has poor directional resolution compared with advanced methods such as those based on maximum likelihood and maximum entropy. Transformations are developed for applying the advanced methods and working with directional wave information stored in the WMO's FM 65 WAVEOB code, the FWGP's Wave Data Analysis Standard (WDAS) format, and similar codes and formats. Using the transformations, a directional Fourier series expansion method, a Maximum Likelihood Method (MLM), and a Maximum Entropy Method (MEM) are each applied to 115 sets of NDBC directional wave data. The MEM and MLM provide better directional resolution, but the MEM produces artificial double peaks. There are considerable differences for the three used methods. The developed transformation equations enable wave data users to apply the method that best suits their applications.

Wave direction analysis from data buoys

This paper describes a new procedure of directional wave analysis from pitch–roll buoy measurements. The two previous procedures adopted by the National Data Buoy Center (NDBC) [Steele, K. E., Lau, J. C. K. and Hsu, Y.-H. L. (1985) Theory and application of calibration techniques for an NDBC directional wave measurement buoy. IEEE Journal of Oceanic Engineering OE-10(4), 382–396; Steele, K. E., Teng, C.-C. and Wang, D. W. C. (1992) Wave direction measurements using pitch–roll buoys. Ocean Engineering 19(4), 349–375] are relevant to our formulations. In these two studies, an estimate for the total phase shift of the sea surface displacement/slope spectra from the measured buoy heave/pitch and heave/roll spectra was calculated either by a weighted average method or a maximum heave/pitch quad-spectrum method. These two formulations were based on a fundamental assumption of symmetric hull-mooring effect on pitch and roll motions, which will never be true in the oceans. In the present study we essentially incorporate the basic formulations of NDBC, but calculate two estimates for this total phase shift. Examples of directional wave analysis from data measured by a 3 m diameter discus buoy during Typhoon Herb are presented in this paper. This data set was also analyzed by the weighted average method of Steele et al. (1985)which yielded unsatisfactory results of wave directions during severe wave climates.

Observations of the Directional Spectrum of Fetch-Limited Waves

Abstract Estimates of the wave directional spectrum of fetch-limited sea states are made from measurements made with a heave–pitch–roll buoy at the Maui location off the west coast of New Zealand. The fetch-limited sea states have significant wave heights between 0.5 and 4.5 m and are observed during persistent southeast wind events, which have a well-defined fetch of 200 km. The integrated properties of the estimated angular spreading distributions are in general agreement with those observed in previous studies. However, the angular distributions estimated for the Maui location are bimodal at frequencies greater than the spectral peak frequency. This result for deep water ocean waves is in contrast to the generally accepted unimodal angular distribution for wind seas, but it supports recently reported measurements of the angular distribution of fetch-limited waves in Lake George, Australia. Parametric relationships that describe the characteristics of the bimodal distributions are derived, and the impor...

Ocean Current Kinematic Effects on Pitch–Roll Buoy Observations of Mean Wave Direction and Nondirectional Spectra

Abstract The effects of ocean surface current Doppler frequency shifting on nondirectional spectra and mean wave direction are modeled. The model does not consider physical wave–current interactions. Model values for both ideal surface-following and 10-m-diameter discus hulls are computed. Unusual wave data reported by a 10-m-diameter discus buoy moored in a strong current in the eastern Gulf of Mexico are also analyzed using the model. Results indicate that the unusual characteristics of the measured data can be explained, at least in part, by the observations being made in a frame of reference (the buoy frame) in motion relative to that in which no ocean current would be observed (the frame moving with the current), provided hull response functions are included and reasonable current directions and speeds are assumed.

Directional Wave Navigation Radar Measurements Compared With Pitch-Roll Buoy Data

Abstract The knowledge of the spectral behavior of a specific sea region is complete when we know surface elevations and directional wave movements. Usually, sea directional descriptions have been made using pitch-roll buoys, which can provide us with several wave characteristic time series. Alternatively, there are other measure systems, which belong to remote sensing technics, such as shipboard navigation radars. The aim of the present work is to compare results obtained from pitch-roll data and ship radar wave measurements obtained during a campaign in the Cantabric Sea.

Radar measurement of directional ocean wave spectra at low incidence angles†

Abstract There exist several techniques for the measurement of directional ocean wave spectra. The most conventional technique is the employment of pitch-roll buoys but a disadvantage of this technique is that it measures at a fixed point. Another promising technique is the use of airborne or spaceborne radars. We present here results of a comparison between the data from an airborne radar, which is measuring near vertical incidence, and measurements of directional wave spectra obtained by means of a pitch-roll buoy and processed by using the Long-Hasselmann iterative algorithm. Although preliminary, these results constitute a step towards the employment of the airborne radar based on the Radar Ocean Wave Spectrometer (ROWS) principle as defined by Jackson (1981), as a validation tool for spaceborne synthetic aperture radars.

Wave direction measurements using pitch-roll buoys

This paper describes the 3-m diameter discus buoys that the National Data Buoy Center for the U.S. National Oceanic and Atmospheric Administration now uses routinely to measure ocean directional wave data. Large quantities of these data, from which estimates of directional wave spectra can be calculated, are now in the national archives. An overview of all aspects of the buoy design is provided, with particular emphasis on data processing methods. A description of a new method for determining the total sensor-hull response phase angle, which needs to be applied each hour to calculate best estimates of directional wave spectra, is included. Examples of measured response functions and directional wave data are presented.

General Analysis of Directional Ocean Wave Data from Heave Pitch Roll Buoys

General Analysis of Directional Ocean Wave Data from Heave Pitch Roll Buoys

General Analysis of Directional Ocean Wave Data from Heave Pitch Roll Buoys

General Analysis of Directional Ocean Wave Data from Heave Pitch Roll Buoys

Multimodal Properties of the Surface-Wave Field Observed with Pitch-Roll Buoys During GATE

Abstract A sophisticated analysis technique is applied to a subset of pitch-roll buoy data collected by the research vessels Gilliss and Quadra during the GARP Tropical Atlantic Experiment (GATE) in September 1974. The procedure enables the examination of directional properties of the wave field at a level of detail not previously along 44°N latitude. BY comparing properties of the observed spectra with the predictions of a simple schematic model of the storm, we conclude that swell reaching the GATE area was emitted during the first half of the storm's lifetime; swell subsequently radiated from the storm was heavily attenuated, either by sheltering of the site by the Cape Verde Islands or because of radically lower emission levels from the storm itself. This work illustrates the power, as well as the limitations of the pitch-roll buoy when used in conjunction with a fully effective analysis technique.

The Surface Wave Environment In the GATE B/C Scale—Phase III

Abstract The surface wave environment in the GATE B/C scale is described from wave measurements made from buoys and aircraft during Phase III (September 1974). Particular emphasis is given to the wave measurements made from the pitch-roll buoy deployed in the B-scale array from the ship Gilliss and a similar buoy deployed in the C-scale array from Quadra. Reduction of the pitch-roll buoy measurements provided estimates of the one-dimensional wave spectrum as well as of the mean direction and spread of wave energy as a function of frequency. The data clearly revealed the importance of external forcing on the wave climate in GATE. Most of the wave energy present in the GATE areas was found to be swell imported from the trade wind circulations of both hemispheres and from an intense extratropical cyclone which crossed the North Atlantic at high latitudes early in Phase III. Locally generated waves were clearly evident in the wave spectra, but their energy level way have been modulated significantly by the lo...

Ocean wave heights measured by a high resolution pulse-limited radar altimeter

Radar measurements of wave height are compared with independent measurements made during the JONSWAP-2 experiment by Waverider and pitch-roll buoys, a shipborne wave recorder and a laser profilometer. The radar data were recorded by a Naval Research Laboratory (NRL) nanosecond-pulse X-band radar altimeter flown in a NASA C-54 aircraft at 3-km altitude under various wind and sea conditions. Averages of 800 pulses of the pulse-limited altimeter data were used to calculate maximum-likelihood estimates of significant wave height (SWH) and skewness of the sea-surface height distribution. The mean values of the radar-estimated SWH were in good agreement with the other measurements. The standard deviation of the values of the radar measurements was typically 10% of the average wave height. A two-dimensional computer simulation of the sea surface indicates that the major portion of the observed standard deviation is attributable to the relatively small sea-surface area illuminated by the radar (125 m × 900 m) rather than to instrumental error. Increasing the number of pulses averaged reduced the variance in the estimates without changing the means. The mean value of the skewness parameter was generally near zero but the standard deviation was typically 0.25. The estimate of SWH did not change when the skewness parameter was constrained to zero.